A TO Z OF PHYSICS“ T A K E U P O N E I D E A . M A K E T H A T O N E I D E A Y O U R L I F E - T H I N K O F I T , D R E A M O F I T , L I V E O N

T H A T I D E A . L E T T H E B R A I N , M U S C L E S , N E R V E S , E V E R Y P A R T O F Y O U R B O D Y , B E F U L L O F T H A T I D E A , A N D J U S T L E A V E E V E R Y O T H E R I D E A A L O N E . T H I S I S T H E W A Y T O S U C C E S S , T H A T I S W A Y

G R E A T S P I R I T U A L G I A N T S A R E P R O D U C E D . ”

What are Units.

In my previous post, I explained with examples how to solve the problems in physics.

To solve problems and to under stand the basics of the Physics it is very important to know what is a

physical quantity, types of physical quantities.What is a unit, what are the units of different physical

quantities, types of units, symbols of units.

There is"one and only one" branch of science which measures a physical quantity, that branch of science

is “Physics”. Measurements have an important role not only in physics, but also in every branch of

science and everywhere in our day-to-day life.

To measure physical quantities we need units. Let’s try to understand necessity of measurements and

"units of measurements" in Physics.

The information about a physical quantity, by description of its external properties like color, taste etc is

incomplete with out knowing its temperature, size (dimensions), which depends on measurement, i.e.

with out measurements it is impossible to know completely about the external properties of any object.

So, it becomes necessary to measure it.

As we know, to measure a physical quantity we require a unit. Different physical quantities will have

different units.

What is unit? A standard reference of the same physical quantity is essential to measure any physical

quantity. That standard which we use to measure a physical quantity is called unit.

Let me put it this way, if we want to measure length of a table, we have to select a standard length

(length of our hand), and by comparing the table’s length with the standard length we can measure the

length of the table. If the table is 3.5 times that of standard length, i.e. length of our hand then we can

write the result as “length of table = 3.5 times the length of our hand or 3.5 units. In this example length

of hand is taken as standard length or unit to measure the table’s length.

Like that we can define any convenient standard or unit to measure a physical quantity.

But, if we choose a standard as in the above example which is not consistent, can not be reproduced.

Because of such undefined units, errors and confusion in measurements will creep in. To avoid such

confusion, instead of taking any undefined reference as a standard, well-defined and universal standards

are used. Such a well-defined reference taken a standard is generally called a well defined unit or unit.

Measurement of every physical quantity will have two parts, a number (n) followed by a unit (u).

There fore n u = constant.

Ex: If the length of a table is 1.2 meters.In this measurement number n= 1.2 and unit is meter.

→ length (L)=n1u1 = 1.2 meters

→ length (L)=n2u2 = 120 centimeters

→ length (L)=n3u3= 1200 millimeters

From the above data we can understand that

i) we can measure a physical quantity in different units.what ever may be the unit it’s value is same.

→ L = n1u1= n2u2 = n3u3

ii) If the unit chosen smaller ,the multiple number will be greater.

→ u1>u1>u1 ==> n1<n2<n3

nu = constant ==> n1u1=n2u2 or u proportional to 1/n

or n proportional to 1/u

==>n1 /n2 = u2/ u1

Generally we can use any convenient unit to measure a physical quantity depending on how much

magnitude we are measuring or in which system of units we want to measure it.

What kind of unit we should use?

The unit i) must be accepted internationally.ii) Should be reproducible.iii) Should be invariable.iv) Should

be easily available.v) Should be consistent.vi) Should be large, if the physical quantity to be measured is a

big quantity.

Ex: To measure larger lengths we use units like Km, mt etc, to measure large magnitude of time

we use units like hour , day ,week, month , year etc.

vii) Should be small if the physical quantity to be measured is small.

Ex: To measure small magnitude time, we use units like millisecond, microsecond etc

To measure small lengths we use units like millimeter, centimeter etc.

Types of physical Quantities.:

We can broadly divide the physical quantities in to two types i)Fundamental Physical quantities ii)Derived

physical quantities.

Fundamental physical quantities: A physical quantity which can exist independently is called

Fundamental physical quantity.

Ex: Length, mass and time etc.

Derived physical quantities: A physical quantity which can not exist independently is called derived

physical quantity. (Or) A physical quantity which is dependent or derived from any other physical

quantity is called derived physical quantity.

Ex : Area, volume, density, speed, acceleration, force, energy etc.

Like the physical quantities, we can Divide the units in to two types.

i)Fundamental units ii)derived units.

Fundamental units : The units of fundamental physical quantities are called fundamental units, (or) The

units which are independent or can not derived from any other unit is called fundamental unit.

Ex:Every unit of length is fundamental unit (irrespective of the system to which it belongs); millimeter,

centimeter, meter, kilometer etc.

Every unit of time is a fundamental physical quantity ; microsecond, millisecond, second, minute, hour,

day etc.

Derived units: The units of derived physical quantities are called derived units. Ex: Units of area,

volume, speed, density, energy etc are derived units.

Ex: Every unit of speed is a derived unit ; m/sec, cm/sec, km/hr etc.

Every unit of density is a derived unit; kg/m³, gr/cm³ etc.

Every unit of acceleration is a derived unit; m/sec², cm/sec², km/hr² etc.

Systems of units: To measure the fundamental physical quantities Length, Mass and time we have three

systems of units, they are i) C.G.S System (Metric system) ii)F.P.S System (British system) and iii)M.K.S

System. In all these three systems only three physical quantities length, mass and time are considered to

be fundamental quantities.

But, in systems Internationale (S.I) system there are seven fundamental physical quantities. Which are

i)Length ii)Mass iii)Time iv)Electric current v) Thermodynamic temperature vi)Luminous intensity

vii)Quantity of substance.

In addition to these two more quantities were added as supplementary physical quantities. They are

i)Plane angle ii)Solid angle.

Systems,Fundamental physical quantities and their units: In

C.G.S system: Length (centimeter); Mass (gram); Time (second).

F.P.S system :Length (foot);Mass(pound);Time (second).

C.G.S system: Length (meter); Mass (kilogram); Time (second).

S.I System:Length (meter); Mass (kilogram); Time (second); Electric current (ampere); Thermodynamic

temperature (kelvin); Intensity of light (candela); Quantity of matter (mole). The units of suplimentary

quantities are Plane angle( radian); Solid angle(Steradian).

Units in different systems.Generally we can use any convenient unit to measure a physical quantity depending on how much

magnitude we are measuring or in which system of units we want to measure it.

What kind of unit we should use?

The unit i) must be accepted internationally.

ii) Should be reproducible.

iii) Should be invariable.

iv) Should be easily available.

v) Should be consistent.

vi) Should be large, if the physical quantity to be measured is a big quantity.

Ex: To measure larger lengths we use units like Km, mt etc, to measure large magnitude of time we use

units like hour , day ,week, month , year etc.

vii) Should be small if the physical quantity to be measured is small.

Ex: To measure small time we use units like millisecond, microsecond etc

To measure small lengths we use units like millimeter, centimeter etc.

Types of physical Quantities.:

We can broadly divide the physical quantities in to two types i)Fundamental Physical quantities ii)Derived

physical quantities.

Fundamental physical quantities: A physical quantity which can exist independently is called

Fundamental physical quantity.

Ex: Length, mass and time etc.

Derived physical quantities: A physical quantity which can not exist independently is called derived

physical quantity. (Or) A physical quantity which is dependent or derived from any other physical

quantity is called derived physical quantity.

Ex : Area, volume, density, speed, acceleration, force, energy etc.

Like the physical quantities we can divide the units in to two types. I)Fundamental units ii)derived units.

Fundamental units : The units of fundamental physical quantities are called fundamental units, (or) The

units which are independent or can not derived from any other unit is called fundamental unit.

Ex:Every unit of length is fundamental unit (irrespective of the system to which it belongs);millimeter,

centimeter, meter, kilometer etc.

Every unit of time is a fundamental physical quantity ; microsecond, millisecond, second, minute, hour,

day etc.

Derived units: The units of derived physical quantities are called derived units. Units of area, volume,

speed, density, energy etc are derived units.

Ex: Every unit of speed is a derived unit ; m/sec, cm/sec, km/hr etc.

Every unit of density is a derived unit; kg/m³, gr/cm³ etc.

Every unit of acceleration is a derived unit; m/sec², cm/sec², km/hr² etc.

Systems of units: To measure the fundamental physical quantities Length, Mass and time we have three

systems of units, they are i) C.G.S System (Metric system)ii)F.P.S System (British system) and iii)M.K.S

System. In all these three systems only three physical quantities length, mass and time are considered to

be fundamental quantities.

But, in systems International (S.I) system there are seven fundamental physical quantities. Which are

i)Length ii)Mass iii)Time iv)Electric current v)Thermodynamic temperature vi)Luminous intensity

vii)Quantity of substance.

In addition to these two more quantities were added as supplementary physical quantities. They are

i)Plane angle ii)Solid angle.

Systems,Fundamental physical quantities and their units:In

C.G.S system: Length (centimeter); Mass (gram); Time (second).

F.P.S system :Length (foot);Mass(pound);Time (second).

C.G.S system: Length (meter); Mass (kilogram); Time (second).

S.I System:Length (meter); Mass (kilogram); Time (second); Electric current (ampere); Thermodynamic

temperature (kelvin); Intensity of light (candela); Quantity of matter (mole). The units of suplimentary

quantities are Plane angle( radian); Solid angle(Steradian).

Multiples,sub multiples of units.

Multiples and sub multiples of Units in S.I system :Depending upon the magnitudes of physical quantities we measure, 

we have to use different multiplication factors suitable for that particular case.Here let us see some widely used multiplication factors.

Multiplication Factor

Prefix symbol

deci d

centi c

milli m

micro

nano n

pico p

femto f

deca da

hecta h

kilo K

mega M

giga G

tera T

peta P

Special Units Of Physical Quantities.

1. Length: a) Micron(  )=  m =   cm

b) Angstrom (A) =  m =  cm

c) Fermi =  m =  cm

d)Astronomical Unit (A.U) = 1.5  m = 1.5  cm

e)X ray unit (X.U) =  m (wave length of X-Rays)

f) Light year = Distance traveled by light in one year=  m = km

g ) parsec = 3.26 light years =  m

2.Time :

a ) Solar day def: The time taken by earth to complete one rotation about its own axis with respect to sun is called solar day. ( Average value for all the days of one year is Mean solar day).

b)Siderial day : It is 4.1min shorter than Mean solar day .

c )siderial year :365.26 Mean solar day d ) Solar year = 365.24 Mean solar day

e )Lear year = The year in which February month has 29 days is called leap year.It is divisible by 4.

f)Lunar month :Time taken by moon to complete one rotation around earth is lunar month = 27.3 days.

3. Mass : a ) Atomic mass Unit ( a.m.u) : =  of mass of   atom =  =   gr =  gr =  kg.

4.Pressure : a ) Atmosphere =760 mmHg =   dyne/  =   dyne/  =  or pa.

b ) Bar = 750 mmHg =   dyne/ =   dyne/  =  or pa.

c) Torr =1 mm Hg =  dyne/ =1333 dyne/ =133N/  or pa.

5.Area : Barn: this is unit of area,it is used to measure cross section of nuclei.

Barn =  

6.Horse Power : It is the British Unit of power =746 w.

Dimensions-Dimensional formulae.

Dimensions :   Dimensions of a physical quantity are,the powers to which the fundamental units are raised to get one unit of the physical quantity.

The fundamental quantities are expressed with following symbols while writing dimensional formulas of derived physical quantities.

Mass →[M] ; Length→[L]; Time→[T]; Electric current →[I] ; Thermodynamic temperature →[K] ;Intensity of light →[cd] ; Quantity of matter →[mol] .

Dimensional Formula :Dimensional formula of a derived physical quantity is the “expression showing powers to which different fundamental units are raised”.

Ex : Dimensional formula of Force F →[ ]

Dimensional equation:When the dimensional formula of a physical quantity is expressed in the form of an equation by writing the physical quantity on the left hand side and the dimensional formula on the right hand side,then the resultant equation is called Dimensional equation.

Ex: Dimensional equation of Energy is E = [ ] .

Question : How can you derive Dimensional formula of a derived physical quantity.

Ans : We can derive dimensional formula of any derived physical quantity in two ways

i)Using the formula of the physical quantity : Ex: let us derive dimensional formula of Force .

Force F→ma ; substitute the dimensional formula of mass m →[M] ; acceleration →[ ]

we get F → [M][ ]; F →[ ] .

ii) Using the units of the derived physical quantity. Ex: let us derive the dimensional formula of momentum.

Unit of Momentum ( p ) → [ ] ;

kg is unit of mass → [M] ; is unit of length → [L] ; sec is the unit of time →[T]

Substitute these dimensional formulas in above equation we get p →[ ].

• Quantities having no units, can not possess dimensions: Trigonometric ratios, logarithmic functions, exponential functions, coefficient of friction, strain, poisson’s ratio, specific gravity, refractive index, Relative permittivity, Relative permeability. All these quantities nighter possess units nor dimensional formulas.

• Quantities having units, but no dimensions : Plane angle,angular displacement, solid angle.These physical quantities possess units but they does not possess dimensional formulas.

• Quantities having both units & dimensions : The following quantities are examples of such quantities.

Area, Volume,Density, Speed, Velocity, Acceleration, Force, Energy etc.

Physical Constants : These are two types

i) Dimension less constants (value of these constants will be same in all systems of units): Numbers, pi, exponential functions are dimension less constants.

ii)Dimensional constants(value of these constants will be different in different systems of units): Universal gravitational constant (G),plank’s constant (h), Boltzmann’s constant (k), Universal gas constant (R), Permittivity of free space( ) , Permeability of free space ( ),Velocity of light (c).

Principle of Homogeneity of dimensions: The term on both sides of a dimensional equation should have same dimensions.This is called principle of Homogeneity of dimensions. (or) Every term on both sides of a dimensional equation should have same dimensions.This is called principle of homogeneity of dimensions.

Uses of Dimensional equations : dimensional equations are used i) to convert units from one system to another,

ii)to check the correctness of the dimensional equations iii)to derive the expressions connecting different physical quantities..

Limitations of dimensional method: The limitations of dimensional methods are

i)The value of dimensionless constants can not be calculated using dimensional methods,

ii)We can not analyze the equations containing trigonometrical, exponential and logarithmic functions using method of dimensions.

iii)If a physical quantity is sum or difference of two or more than two physical quantities, such physical quantities can not be derived with dimensional methods,

iv)If any equation having dimensional constants like, G, R etc can not be derived using dimensional methods,

v)If any equation is involving more than three fundamental quantities in it, such expressions can not be derived using dimensional methods.

Table of Units,dimensional Formulas of physical quantities.Fundamental Physical Quantities:

S.NoFundamental Physical

Quantity

FormulaDimensional

Formula

S.I Unit of physical quantity

1.Mass

Amount of matter in the object

Mkg

2. Length L meter

3. Time T sec

4. Electric current I or A ampere

5. Amount of substance N mole(mol)

6. Luminous intensity J candela(cd)

7. Temperature K or  Kelvin

Derived Physical Quantities:

S.No Derived Physical Quantity FormulaDimensional

FormulaS.I Unit of physical

quantity

1. Area [ ]

2. Volume [ ]

3. Density [ ]

4. Specific Gravity [ ] No units

5. Frequency [ ] hertz

6. Angle No units

7. Velocity m/sec

8. Speed m/sec

9. Areal velocity

10. Acceleration

11. Linear momentum kg m/sec

12. Force kg-m/  or Newton

13. Weight w=mg kg-m/  or Newton

14. Moment of force/Torque/Couple kg

15. Impulse kg m/sec or Ns

16. Pressure N/  or Pa

17. Work Nm or Joule

18. Kinetic Energy joule

19. Potential Energy mgh joule

20. Gravitational constant

21. Gravitational field strength

22. Gravitational Potential

23. Force constant (k)

24. Power W or J/sec

25. Moment of Inertia ( I ) kg

26. Stress N/  or Pa

27. Strain No units

28. Modulus of Elasticity N/  or Pa

29. Poission’s Ratio σ = -1 No units

30. Velocity gradient

31. Coefficient of dynamic viscosity kg (or) N-sec/$latex  \m^2$

(or)pascal-sec (or)poiseuille

32. Surface Tension ,N/m

33. Angular displacement ( ) no Units

34. Angular velocity(ω) rad/sec

35. Angular acceleration(α) rad/

36. Angular momentum Iω

37. Angular Impulse Iω

38. Temperature  or K kelvin or degree Celsius

39.Coefficient of linear expansion(α)

/kelvin

40. Specific heat

41. Latent heat

42. Entropy

43. Thermal capacity

44. Gas constant

45.coefficient of thermal conductivity

46. Pole strength Am

47. Magnetic Moment

48. Magnetic flux  weber ; ;J/Amp

49.Magnetic field,magnetic flux density (B) Tesla;

50. Permeability of free space

51.Magnetic susceptibilty also called volumetric or bulk susceptibility χm

χm = μr − 1 no units

52. Electric Charge Amp sec , coul

53. Electric potential Volt

54. E.M.F Volt

55. Electric Capacity Farad

56. Electric Resistance Ohm (Ω) or volt/amp

57. Resistivity  Ohm mt (Ω-m)

58. Conductivity  1/ Siemens/m

59. Permittivity  farad/m

60. Electric conductance Siemens (or) mhos

61. Electric power Watt

62. Electrical Impedance(Z) Ohm (Ω) or volt/amp

63. Electrical admittance 1/Z(Reciprocal of electric impedance) Siemens (or) mhos

64. Self Inductance(L) weber/amp or Henry

65. Boltzmann’s constant J/kelvin

66. Stefan’s constant

67. Co-efficient of friction  = ,N=Normal reactiondimension less scalar

no units

68. Dielectric constant  It is also called relative permittivity dimension lessnounits

69. Planck’s constant J.sec (or) eV.sec

70. Refractive index μ no units

71. Focal length(f)Distance between center of the lens(mirror) to

its focusL meter

72. Power of a lens (P)The reciprocal of the focal length of a lens in

meters is called power of a lens; p=1/fdiaptors

73. Wave number No.of waves/distance

74. Wave length Length of a wave L meter

units-Dimensions ( QA)

1. What is a physical quantity?

Ans : Any quantity which is measurable is called physical quantity.

2. Explain the term Fundamental Physical quantity.

Ans: The physical quantity which is independent or which can not be derived from any other physical quantity is called fundamental physical quantity. EX: Mass, Length and Time.

3.Explain the term Derived physical quantity.Give examples.

Ans :The physical quantity which is dependent on other physical quantity or which is derived from other physical quantity is called derived physical quantity. Ex : Area, Electric charge, Magnetic field strength, power etc.

4.How many fundamental quantities are there in C.G.S; F.P.S and M.K.S systems? What are they?

Ans : There are 3 fundamentals quantities in C.G.S; F.P.S and M.K.S systems, they are mass, length and time.

5.How many fundamental quantities are there in S.I systems? What are they?

Ans : In S.I system 7 fundamental quantities are there,they are i) Mass ii)Length iii)Time iv)Electric current v)Intensity of light vi) Thermodynamic temperature vii) Quantity of matter.

6.How many supplementary quantities are there in S.I system? What are they?

Ans : In S.I system there are 2 supplementary quantities, they are i) Plane Angle ii) Solid Angle.

7. What are the units of length in C.G.S ; F.P.S and M.K.S systems.

Ans : The units of length are cm,foot and meter respectively in C.G.S ; F.P.S and M.K.S systems .

8. what are the units of fundamental quantities in S.I system?

Ans : Mass → kg ; Length → m ; Time → sec ; Electric current → Amp Thermodynamic temperature → kelvin ;

Intensity of light → candela ; Quantity of matter → mole .

9.what are the units of supplementary quantities in S.I system?

Ans : Plane angle → radian ; Solid angle → steradian .

10. Name the physical quantities whose dimensional formula is   ?

Ans : The physical quantities are i)Distance or length ii) displacement iii)wave length

11. Name the physical quantities whose dimensional formula is   ?

Ans : The physical quantities are i) speed ii) velocity

12.Name the physical quantities whose dimensional formula is   ?

Ans : The physical quantities are i)Thermal capacity ii) Entropy

13. Name the physical quantities whose dimensional formula is   ?

Ans : The physical quantities are i)Momentum ii) impulse .

14.Name the physical quantities whose dimensional formula is   ?

Ans : The physical quantities are i)force ii ) Tension iii) weight .

15.Name the physical quantities whose dimensional formula is   ?

Ans : The physical quantities are i) Work ii) Energy iii) Heat iv)Moment of force Iv) Torque .

16.Name the physical quantities whose dimensional formula is  ?

Ans : The physical quantities are i) pressure ii ) stress iii) Young’s modulus iv) Rigidity modulus v) Bulk modulus .

17.Name the physical quantities whose dimensional formula is   ?

Ans : The physical quantities are i) frequency ii) Decay constant iii)Angular velocity .

18 . Name the physical quantities whose dimensional formula is   ?

Ans : The physical quantities are i )angular momentum ii )Plank constant .

19. Name the physical quantities whose dimensional formula is   ?

Ans : The physical quantities are i )Force constant ii )surface tension .

20. Which physical quantity has negative dimensions in mass ?

Ans : Gravitational constant (G) .

21. State few constants which have dimensions ?

Ans : i) Plnak’s constant (h) ii)Velocity of light in vacuum (c) iii)Permeability of free space ( ) iv) Permittivity of free space ( ) v)Universal gravitational constant (G) vi) Universal gas constant (R)

vii)Boltzmann constant (k) .

22 .which physical quantities have the unit henry ?

Ans : self Inductance and Mutual Inductance have the unit henry .

units-Dimensions ( QA)

23. What are the dimensions of electric conductivity in mass , length and current.

Ans : Electric conductivity has -1,-3 and 2 dimensions in mass,length and current respectively.

24. What is the unit of electric conductivity in C.G.S and S.I systems?

Ans : It has no unit in C.G.S system ; its unit in S.I system is Siemen/meter or S/m.

25.What are the uses of Dimensional methods?

Ans : To convert units from one system to another. ii )To check the correctness of equations connecting physical quantities iii )To derive the expressions connecting physical quantities.

26. Which is the physical quantity whose S.I unit is Am ?

Ans: Magnetic pole strength.

27. V/m or N/Coulomb are the units of ……. Physical quantity.

Ans : These are the units of Electric field strength.

28.Name five physical quantities which neither have dimensions nor units.

Ans : Refractive Index , specific gravity,susceptibility,dielectric constant, coefficient of friction.

29. If V = Xt+Y ; V is the velocity , t is time.What are the dimensional formulas of X and Y ?

Ans : According to principle of homogeneity of dimensions, the dimensions of M,L and T in every term should be same.

Therefore   = X   → X =   ; X →   and Y→ 

30.Which physical quantities does not possess dimensions in mass ?

Ans :Area,volume, velocity, acceleration,angular displacement, angular velocity, angular acceleration.

units-Dimensions ( QA)

23. What are the dimensions of electric conductivity in mass , length and current.

Ans : Electric conductivity has -1,-3 and 2 dimensions in mass,length and current respectively.

24. What is the unit of electric conductivity in C.G.S and S.I systems?

Ans : It has no unit in C.G.S system ; its unit in S.I system is Siemen/meter or S/m.

25.What are the uses of Dimensional methods?

Ans : To convert units from one system to another. ii )To check the correctness of equations connecting physical quantities iii )To derive the expressions connecting physical quantities.

26. Which is the physical quantity whose S.I unit is Am ?

Ans: Magnetic pole strength.

27. V/m or N/Coulomb are the units of ……. Physical quantity.

Ans : These are the units of Electric field strength.

28.Name five physical quantities which neither have dimensions nor units.

Ans : Refractive Index , specific gravity,susceptibility,dielectric constant, coefficient of friction.

29. If V = Xt+Y ; V is the velocity , t is time.What are the dimensional formulas of X and Y ?

Ans : According to principle of homogeneity of dimensions, the dimensions of M,L and T in every term should be same.

Therefore   = X   → X =   ; X →   and Y→ 

30.Which physical quantities does not possess dimensions in mass ?

Ans :Area,volume, velocity, acceleration,angular displacement, angular velocity, angular acceleration.

WIKKIPEDIA NOTES:

This is a list of physical quantities.

The first table lists the base quantities used in the International System of Units to define the physical dimension of physical quantities for dimensional analysis. Note that the angle and solid angle are included in this list but are actually dimensionless quantities. The second table list the other physical quantities.

Note :- neither the names nor the symbols used for the physical quantities are international standards. Some quantities are known as several different names such as the magneticB-field which known as the magnetic flux density, the magnetic induction or simply as the magnetic field depending on the context. Similarly, surface tension can be denoted by either σ, γ or T. The table usually list only one name and symbol.

Base quantity

Symbol

Description SI unitSymbol for dimension

Comments

Length l The one dimensional extent of an object. metre (m) L

Mass m The amount of matter in an object.kilogram (kg) M extensive

Time t The duration of an event. second (s) T

Electric current

I Rate of flow of electrical charge. ampere (A) I

Temperature TAverage energy per degree of freedom of a system.

kelvin (K) Θ intensive

Amount of substance

nNumber of particles compared to the number of atoms in 0.012 kg of12 C .

mole (mol) N extensive

Luminous intensity

LAmount of energy emitted by a light source in a particular direction.

candela (cd) J

Derived quantity

Symbol

Description SI units Dimension Comments

(Mass) Density (volume density)

ρThe amount of mass per unit volume of a three dimensional object.

kg m−3 M L−3 intensive

(Radioactive) Activity

ANumber of particles decaying per unit time.

becquerel (Bq = s−1) T−1 extensive

(Radioactive) Dose D

Amount of energy absorbed by biological tissue from ionizing radiation per unit mass.

gray (unit) (Gy = m2s−2)

L2 T−2

Absorbed dose rate

Absorbed dose received per unit of time.

Gy s−1 L2 T−3

Acceleration aRate of change of the speed or velocity of an object.

m s−2 L T−2 vector

Angular acceleration

αRate of change in angular speed or velocity.

rad s−2 T−2

Angular momentum L

Measure of the extent and direction and object rotates about a reference point.

kg m2 s−1 M L2 T−1conserved quantity, pseudovector

Angular speed (orangular velocity)

ω or ω

The angle incremented in a plane by a segment connecting an object and a reference point.

rad s−1 T−1 scalar or pseudovector

Area A The two dimensional extent m2 L2

Derived quantity

Symbol

Description SI units Dimension Comments

of an object.

Area density ρA

The amount of mass per unit area of a two dimensional object.

kg m−2 M L−2

Capacitance CMeasure for the amount of stored charge for a given potential.

farad (F = A2 s4 kg−1m−2) I2 T4 M−1 L−2

Catalytic activityChange in reaction rate due to presence of a catalyst.

katal (kat = mol s−1) N T−1

Catalytic activity concentration

Change in reaction rate due to presence of a catalyst per unit volume of the system.

kat m−3 N L−3 T−1

Chemical potential μThe amount of energy needed to add a particle to a system.

J mol−1 M L2 T−2 N−1 intensive

Current density JAmount of electric current flowing through a surface.

A m−2 I L−2

Dose equivalent H

Measure for the received amount of radiation adjusted for the effect of different types of radiant on biological tissue.

sievert (Sv = m2 s−2) L2 T−2

Dynamic Viscosity ηMeasure for the resistance of an incompressible fluid to stress.

Pa s M L−1 T−1

Electric Charge Q Amount of electric charge.coulomb (C = A s) I T

extensive, conserved quantity

Electric charge density

ρQAmount of electric charge per unit volume.

C m−3 I T L−3 intensive

Electric displacement

DStrength of the electric displacement.

C m−2 I T L−2 vector field

Derived quantity

Symbol

Description SI units Dimension Comments

Electric field strength

E Strength of the electric field. V m−1 M L T−3 I−1 vector field

Electric potential V

The amount of work required to bring a unit charge into an electric field from infinity.

volt (V = kg m2 A−1 s−3) L2 M T−3 I−1 scalar

Electrical conductance

GMeausure for how easily current flows through a material.

siemens (S = A2 s3kg−1 m−2) L−2 M−1 T3 I2 scalar

Electrical resistance

RThe degree to which an object opposes the passage of an electric current.

ohm (Ω = kg m2 A−2s−3) L2 M T−3 I−2 scalar

Energy EThe capacity of a body or system to do work.

joule (J = kg m2 s−2) M L2 T−2

extensive, scalar, conserved quantity

Energy density ρEAmount of energy per unit volume.

J m−3 M L−1 T−2 intensive

Entropy SMeasure for the amount of available states for a system.

J K−1 M L2 T−2 Θ−1 extensive, scalar

Force FThe cause of acceleration, acting on an object.

newton (N = kg m s−2) M L T−2 vector

Frequency fThe number of times something happens in a period of time.

hertz (Hz =s−1) T−1

Half-life t1/2

The time needed for a quantity to decay to half its original value.

s T

Heat Q

Amount of energy transferred between systems due to temperature difference.

J M L2 T−2

Heat capacity Cp Amount of energy needed to J K−1 M L2 T−2 Θ−1 extensive

Derived quantity

Symbol

Description SI units Dimension Comments

raise the temperature of a system by one degree.

Heat flux density ϕQ

Amount of heat flowing through a surface per unit area.

W m−2 M T−3

Illuminance EvTotal luminous flux incident to a surface per unit area.

lux (lx = cd sr m−2) J L−2

Impedance Z

Measure for the resistance of an electrical circuit against an alternating current.

ohm (Ω = kg m2 A−2s−3) L2 M T−3 I−2 complex scalar

Impulse pThe cause of a change in momentum, acting on an object.

kg m s−1 M L T−1 vector

Index of refraction nThe factor by which the speed of light is reduce in a medium.

1 intensive

Inductance L

Measure for the amount of magnetic flux generated for a certain current run through a circuit.

henry (H = kg m2 A−2s−2) M L2 T−2 I−2

Irradiance EPower of electromagnetic radiation flowing through a surface per unit area.

W m−2 M T−2

Linear density ρl

Amount of mass per unit length of a one dimensional object.

M L−1

Luminous flux (orluminous power)

FPerceived power of a light source.

lumen (lm = cd sr) J

Magnetic field strength

HStrength of a magnetic field in a material.

A m−1 I L−1 vector field

Magnetic flux Φ Measure of quantity weber (Wb = M L2 T−2 I−1 scalar

Derived quantity

Symbol

Description SI units Dimension Comments

of magnetism, taking account of the strength and the extent of a magnetic field.

kg m2 A−1s−2)

Magnetic flux density

BMeasure for the strength of the magnetic field.

tesla (T = kg A−1 s−2) M T−2 I−1 pseudovector

field

Magnetization MAmount of magnetic moment per unit volume.

A m−1 I L−1 vector field

Mass fraction xMass of a substance as a fraction of the total mass.

kg/kg 1 intensive

Mean lifetime τAverage time needed for a particle to decay.

s T intensive

Molar concentration

CAmount of substance per unit volume.

mol m−3 N L−3 intensive

Molar energyAmount of energy present is a system per unit amount of substance.

J mol−1 M L2 T−2 N−1 intensive

Molar entropyAmount of entropy present in a system per unit amount of substance.

J K−1 mol−1 M L2 T−2 Θ−1 N−1 intensive

Molar heat capacity

cHeat capacity of a material per unit amount of substance.

J K−1 mol−1 M L2 T−2 N−1 intensive

Moment of inertia IInertia of an object with respect to angular acceleration.

kg m2 M L2 tensor

Momentum pProduct of an object's mass and velocity.

N s M L T−1 vector, extensive

Permeability μ

Measure for how the magnetization of material is affected by the application of an external magnetic field.

H m−1 M L−1 I−2 intensive

Derived quantity

Symbol

Description SI units Dimension Comments

Permittivity ε

Measure for how the polarization of a material is affected by the application of an external electric field.

F m−1 I2 M−1 L−2 T4 intensive

Plane angle θMeasure of a change in direction or orientation.

radian (rad) 1

Power PThe rate of change in energy over time.

watt (W) M L2 T−3 extensive

Pressure pAmount of force per unit area.

pascal (Pa = kg m−1s−2) M L−1 T−2 intensive

Radiance L

Power of emitted electromagnetic radiation per solid angle and per projected source area.

W m−2 sr−1 M T−3

Radiant intensity IPower of emitted electromagnetic radiation per solid angle.

W sr−1 M L2 T−3 scalar

Reaction rate rMeasure for speed of a chemical reaction.

mol m−3 s−1 N L−3 T−1 intensive

Solid angle ΩMeasure of the size of an object as projected on a sphere.

steradian (sr) 1

Specific energyAmount of energy present per unit mass.

J kg−1 L2 T−2 intensive

Specific heat capacity

c Heat capacity per unit mass. J kg−1 K−1 L2 T−2 Θ−1 intensive

Specific volume vThe volume occupied by a unit mass of material (reciprocal of density).

m3 kg−1 L3 M−1 intensive

Speed vRate of change of the position of an object.

m s−1 L T−1 scalar

Spin S Intrinsic property of kg m2 s−1 M L2 T−1

Derived quantity

Symbol

Description SI units Dimension Comments

particles, roughly to be interpreted as the intrinsic angular momentum of the particle.

Stress σAmount of force exerted per surface area.

Pa M L−1 T−2 2-tensor. (or scalar)

Surface tension γAmount of work needed to change the surface of a liquid by a unit surface area.

N m−1 or J m−2 M T−2

Thermal conductivity

kMeasure for the ease with which a material conducts heat.

W m−1 K−1 M L T−3 Θ−1 intensive

Torque (moment of force)

τ

Product of a force and the perpendicular distance of the force from the point about which it is exerted.

N m M L2 T−2 pseudovector

Velocity vSpeed of an object in a chosen direction.

m s−1 L T−1 vector

Volume VThe three dimensional extent of an object.

m3 L3 extensive

Wavelength λDistance between repeating units of a propagating wave.

m L

Wavenumber kReciprocal of the wavelength.

m−1 L−1

Weight wAmount of gravitation force exerted on an object.

newton (N = kg m s−2) M L T−2

Work W

Energy dissipated by a force moving over a distance, scalar product of the force and the movement vector.

joule (J = kg m2 s−2) M L2 T−2 scalar

Units and Dimensionality

Basic, Mechanical and Electrical units and conversions

Physics equations for Mechanical and Electrical quantities

Contents

Physical Quantities and their Associated Dimensions Basic Physical Quantities Mechanical Physical Quantities Electrical Physical Quantities The Algebra of Dimensionality Conversion Between Systems of Units Definitions of Fundamental Units Definitions of Derived Units Units Conversion Constants Physical Constants Physics Equations

Just need a numeric conversion from one unit to another: click below

www.easyunitsconverter.com

Physical Quantities and Their Associated Dimensions

Errors can occur in writing equations to solve problems in classicalphysics. Many of these errors can be prevented by performing a dimensionalitycheck on the equations. All physical quantities have a fundamental dimensionthat is independent of the units of measurement. The basic physical dimensionsare: length, mass, time, electrical charge, temperature and luminous intensity.

There are a number of systems of units for measuring physical dimensions. The MKS system is based on meter, kilogram, second measurement. The CGS systemis based on centimeter, gram, second measurement. The English system is basedon feet, pound, second measurement. A few physical dimensions and theassociated measurement unit in these three systems are :

Physical Quantity Unit System Dimension MKS CGS English

length meter centimeter feet

mass kilogram gram pound mass

time second second second

force newton dyne poundal

energy joule erg B.t.u.

The checking of a physical equation has two aspects. The first is to checkthe dimensionality. The dimensionality is independent of the unit system. Thesecond is to check that a consistent system of units is used in the equation.

An example of a dimensionality check is using the basic equation F=ma todetermine that force has the dimension mass x length / time squared, thencheck if F=mv2 /r is dimensionally correct. The check is performed by expanding the dimensions, e.g. mass x (length/time) x (length/time) / length.Combining terms and reducing yields mass x length / time squared. This agreeswith the dimensions expected for force from the basic equation F=ma. Asexpected, centripetal force has the same dimensionality as the force fromNewton's second law of motion.

The table below is organized to present the physical quantity name withassociated information. The second column is one of the typical symbols usedfor the physical quantity. The third column is the dimension of the physicalquantity expressed in terms of the fundamental dimensions. The fourth columnis the name of the unit in the MKS measurement system. The fifth columnis the typical MKS unit equation. An independent table presents conversion

factors from the MKS measurement system to other measurement systems.

Physics developed over a period of many years by many people from a varietyof disciplines. Thus, there is ambiguity and duplication of symbols.

Basic Physical Quantities

PHYSICAL QUANTITY SYMBOL DIMENSION MEASUREMENT UNIT UNIT EQUATION_________________ ______ _________ ________________ ______________

length s L meter m

mass m M kilogram Kg

time t T second sec

electric charge q Q coulomb c

luminous intensity I C candle cd

temperature T K kelvin oK

angle theta none radians none

Mechanical Physical Quantities (derived)

PHYSICAL QUANTITY SYMBOL DIMENSION MEASUREMENT UNIT UNIT EQUATION_________________ ______ _________ ________________ ______________

area A L2 square meter m2

volume V L3 stere m3

velocity v L/T meter per second m/sec

angular velocity ω 1/T radians per second sec-1

acceleration a L/T2 meter per square m/sec2

second

angular acceleration α 1/T2 radians per 1/sec2

square second

force F ML/T2 newton Kg m/sec2

energy E ML2/T2 joule Kg m2 /sec2

work W "

heat Q "

torque T ML2/T2 newton meter Kg m2 /sec2

power P ML2/T3 watt joule/sec

density ρ M/L3 kilogram per Kg/m3

cubic meter

specific gravity SG ratio of density to density of water SG times 1000 Kg/m3 is &rho

pressure P M/LT2 newton per sq m Kg/m sec2

elastic modulus E square meter

bulk modulus K M/LT2 newton per sq m Kg/m sec2

(pressure)stress σ M/LT2 newton per sq m Kg/m sec2

(pressure)

strain ε none (L'-L)/L dimensionless

momentum p ML/T newton second Kg m/sec

impulse p ML/T newton second Kg m/sec

inertia (linear) I ML2/T joule second Kg m2/sec

moment of inertia I ML2 kilogram meter sq Kg m2

luminous flux Φ C lumen (4Pi candle cd sr for point source)

illumination E C/L2 lumen per cd sr/m2

square meter

entropy S ML2/T2 K joule per degree Kg m2 /sec2 oK

volume rate of flow Q L3/T cubic meter m3 /sec per second

dynamic viscosity μ M/LT newton second Kg/m sec per square meter

kinematic viscosity μ/ρ ν L2/T square meter m2 /sec per second

specific weight γ M/L2 T2 newton Kg/m2 sec2

per cubic meter

Electrical Physical Quantities (derived)

PHYSICAL QUANTITY SYMBOL DIMENSION MEASUREMENT UNIT UNIT EQUATION_________________ ______ _________ ________________ ______________

electric current I Q/T ampere c/sec

2 2 2 2emf,voltage,potential E ML /T Q volt Kg m /sec c

2 2 2 2electric resistance R ML /TQ ohm Kg m /sec c

2 3 2 3conductivity sigma TQ /ML mho per meter sec c /Kg m

2 2 2 2 2 2capacitance C T Q /ML farad sec c /Kg m

2 2 2 2inductance L ML /Q henry Kg m /c

2 2current density J Q/TL ampere per c/sec m square meter

3 3charge density rho Q/L coulomb per c/m cubic meter

magnetic flux, B M/TQ weber per Kq/sec c magnetic induction square meter

magnetic intensity H Q/LT ampere per meter c/m sec

magnetic vector potential A ML/TQ weber/meter Kg m/sec c

2 2electric field intensity E ML/T Q volt/meter or Kg m/sec c newton per coulomb

2 2electric displacement D Q/L coulomb per c/m

square meter

2 2permeability mu ML/Q henry per meter Kg m/c

2 2 3 2 2 3 permittivity, epsi T Q /ML farad per meter sec c /Kg m dielectric constant

-1frequency f Pi/T hertz sec

-1angular frequency omega 1/T radians per second sec

wave length lambda L meters m

The Algebra of Dimensionality

The dimension of any physical quantity can be written as

La Mb Tc Qd Ce Kf

where a,b,c,d,e and f are integers such as -4, -3, -2 , -1, 0, 1, 2, 3, 4and L is length, M is mass, T is time, Q is charge, C is luminous intensityand K is temperature. An exponent of zero means the dimension does not applyto the physical quantity. The normal rules of algebra for exponents applyfor combining dimensions.

In order to add or subtract two physical quantities the quantities musthave the same dimension. The resulting physical quantity has the samedimensions. Physical quantities with the same dimension in differentsystems of units can be added or subtracted by multiplying one ofthe quantities by a units conversion factor to obtain compatible units.

The multiplication of two physical quantities results in a new physicalquantity that has the sum of the exponents of the dimensions of the initialtwo quantities.

The division of one physical quantity by another results in a new physicalquantity that has the dimension of the exponents of the first quantity minusthe exponents of the second quantity.

Taking the square root of a physical quantity results in a new physicalquantity having a dimension with exponents half of the initial dimension.

Raising a physical quantity to a power results in a new physical quantity

having a dimension with the exponents multiplied by the power.

e.g. v has dimension L/T then v2 has dimension L2/T2 or L2 T-2

The derivative of a physical quantity with respect to another physicalquantity results in a new physical quantity with the exponents of thefirst dimension minus the exponents of the other dimension.

e.g. v has dimension L/T, t has dimension T, then dv/dt has dimension L/T2 of acceleration

The integral of a physical quantity over the range of another physicalquantity results in a new physical quantity that has a dimension with thesum of the exponents of the two quantities.

e.g. v has dimension L/T, t has dimension T,

then integral v dt has dimension L

Conversion Between Systems of Units

This section is organized to be consistent with the discussion of physicalquantities and equations of physics. The definition of the six fundamentalunits of physical quantities is presented for the MKS system of units. Thedefinition of some derived units is then presented in the MKS system. Thedefinitions in other systems of units follow the MKS definitions. This isfollowed by a table of conversion factors between the MKS system and othersystems of units.

The MKS system based on the meter, kilogram second was augmented to allowforce and energy from electrical quantities to be measured in one rationalizedsystem of units. The system was proposed by Giorgi in 1904. It was adopted bythe IEC in 1935 to take effect on January 1, 1940. The electrical to mechanicalconversion was chosen to be based on the permeability of free space to be

-74Pi x 10 henry per meter.

Definition of Fundamental Units

Meter, fundamental unit of length, defined as the distance between two

ospecified lines on a specific bar of platinum-iridium at 0 C at standardatmospheric pressure supported at two neutral points 0.285 meter from thecenter of the bar. The bar is kept at the International Bureau of Weightsand Measures near Paris France.

Centimeter, cgs unit of length, defined as 1/100 meter.

Feet, English unit of length, defined as 0.3048 meter in U.S.

Inch, English unit of length, defined as 0.00254 meter in U.S.

-10Angstrom, unit of length, defined as 10 meter.

Kilogram, fundamental unit of mass, defined as the mass of a specificcylinder of platinum - iridium kept at the International Bureau of Weights andMeasures.

Gram, cgs unit of mass, defined as 1/1000 kilogram.

Pound, English unit of mass, the avoirdupois pound is defined to be0.4535924277 kilogram in the U.S. The apothecary or troy pound is5760/7000 of the avoirdupois pound.

Second, fundamental unit of time, defined as one 86,400th part of a meansolar day. Presently measured by an atomic clock based on the rate of nucleardecay.

Coulomb, fundamental unit of charge, defined as the charge required toobtain one newton of force between two such charges at a distance of onemeter.

Candle, fundamental unit of luminous intensity, defined as the sourceintensity of 1/60 centimeter square opening of the standard light sourceof a glowing cavity with temperature equal to that of solidifying platinum.A point source of one candle radiates one lumen per steradian.

Kelvin, fundamental unit of temperature, defined as zero where

the molecular activity of gases cease. The scale is based on zero degreescentigrade (Celsius) for the freezing point of water and 100 degreescentigrade at the boiling point of water. Zero degrees centigrade is 273.16Kelvin.

Radians, fundamental unit of angle, defined as the angle formed by alength of circular arc being equal to the radius creating the arc.

Definition of Derived Units

Newton, unit of force, defined as the force required to accelerate a massof 1 kilogram at 1 meter per second per second when acting continuously.

Dyne, cgs unit of force, defined as the force required to accelerate a mass -5of 1 gram at at 1 centimeter per second per second. One dyne is 10 newton.

Poundal, English unit of force, defined as the force required to acceleratea mass of 1 pound at 1 foot per second per second. One poundal is -107.23300 10 newton. A poundal based on earth's gravitation is 32.174 poundsavoirdupois.

Joule, unit of energy, defined as work done by 1 newton acting through adistance of one meter. (equivalent to one watt expended in one second.)

Erg, cgs unit of energy, defined as work done by 1 dyne acting through a -7distance of one centimeter. One erg is 10 joule.

Kilogram calorie, large calorie, unit of energy, is the heat required toraise the temperature of 1 kilogram of water 1 degree centigrade at astated temperature. i.e. Kg Cal(22 C). The mean kilogram calorie is defined as1/100 of the heat required to raise the temperature of 1 kilogram of water o ofrom 0 C to 100 C. The small calorie is the gram calorie equal to 1/1000 ofa large calorie. One mean kilogram calorie is 0.000238889 joule .

British thermal unit, B.t.u , unit of energy, the heat required to raisethe temperature of 1 pound of water 1 degree Fahrenheit at a stated o

temperature. i.e. B.t.u.(39 F). The mean British thermal unit is defined as1/180 of the heat required to raise the temperature of 1 pound of water from o o32 F to 212 F. One mean B.t.u. is 0.00009480 joule.

Mole, kilogram molecule, is the number of kilograms of a substance thatcorresponds to its molecular weight divided by 1000. In the cgs system ofunits a mole, gram molecule, is the number of grams of a substance thatcorresponds to its molecular weight. The mass of a single molecule inkilograms is the kilogram molecule divided by Avogadro's number. For atomsthe molecular weight is the atomic weight.

Steradian, sr, is the ratio of the area of the intercepted surface ofa sphere to the radius of the sphere squared. 4Pi steradians means thetotal area of the sphere is intercepted.

Watt, unit of power, defined as work done at a constant rate of onejoule per second.

Horsepower ( mechanical ), English unit of power, defined as work doneat a rate of 550 foot-pounds per second. One mechanical horsepower is745.705 watt.

Horsepower ( electrical ), English unit of power, by definition exactly760 watt.

Ampere, unit of electric current, defined as the current that will flowthrough a circuit with a resistance of one ohm when one volt is applied. Theinternational standard is defined as the current which will deposit silverat a rate of 0.00111800 gram per second. One international ampere is about0.999835 absolute ampere. International electrical units are based on physicalstandards whose specifications are slightly in error. Instruments made afterJanuary 1, 1948 are calibrated in absolute units.

Notes: The singular form of units is used with the exception of foot and feet. Proper names appearing in units and constants are not capitalized.

References: Conversion Factors and Tables by Zimmerman and Lavine Electric and Magnetic Fields by Stephen Attwood

Elements of Physics by Shortley and Williams

UNITS CONVERSION CONSTANTS

to get MKS units from other units to get other units from MKS units

value value value valuein MKS = in other x constant in other = in MKS x constantunits units units units

length

meter = angstrom x 1.0E-10 angstrom = meter x 1.0E10

meter = mil x 0.254E-4 mil = meter x 39370.07874

meter = centimeter x 0.01 centimeter = meter x 100

meter = inch x 0.0254 inch = meter x 39.37007874

meter = feet x 0.3048 feet = meter x 3.280839895

meter = yard x 0.9144018288 yard = meter x 1.0936111

meter = fathom x 1.8288036 fathom = meter x

meter = rod x 5.0292099 rod = meter x 0.19883839

meter = chain(surveyor) x 20.12 chain(surveyor) = meter x 66 ft

meter = chain(engineer) x 30.48006 chain(engineer) = meter x 100 ft

meter = furlong x 0.2011684E+3 furlong = meter x 0.49709597E-2

meter = mile(statute) x 1.6093472E+3 mile(statute) = meter x 0.6213699E-3 *

meter = mile(nautical) x 1.8532487E+3 mile(nautical) = meter x 0.539593E-3

meter = league(land) x 4.82804E+3 league(land) = meter x

meter = league(marine) x 5.5596E+3 league(marine) = meter x

meter = light year x 9.459936E+15 light year = meter x

mass

kilogram = gram x 0.001 gram = kilogram x 1000

kilogram = grain(troy) x 0.6480E-4 grain(troy) = kilogram x 15432

kilogram = pennyweight(troy) x 1.5552E-3 pennyweight(troy) = kilogram x 643 pennyweight(troy) = grains * 24

kilogram = carat(troy) x 0.2E-3 carat(troy) = kilogram * 5000 carat(troy) = grains * 324

kilogram = scruple x 1.296E-3 scruple = kilogram x 771.6

kilogram = dram(avdp) x 1.772E-3 dram(avdp) = kilogram x 564.334

kilogram = ounce(avdp) x 0.02834952 ounce(avdp) = kilogram x 35.27

kilogram = ounce(troy) x 0.031103481 ounce(troy) = kilogram x 32.15

kilogram = pound(troy) x 0.37324177 pound(troy) = kilogram x 2.6792285

kilogram = pound(avdp) x 0.45359244 pound(avdp) = kilogram x 2.204622341 *

kilogram = ton(short) x 907.18486 ton(short) = kilogram x 1.102311E-3 ton(short) = 2000 pounds(avdp) *

kilogram = ton(long) x 1016.047 ton(long) = kilogram x 0.9842064E-3

kilogram = ton(metric) x 1000 ton(metric) = kilogram x 0.001

time

second = minute x 60 minute = second * 0.0166667

second = hour x 3600 hour = second * 2.777778E-4

second = day x 86400 day = second * 1.1574E-5

second = fortnight x 1.2096E+6 fortnight = second * 0.82672E-6

second = month x 2.6298E+6 month = second * 0.380257E-6

second = year x 31.557E+6 year = second * 0.031688E-6

electric charge

coulomb = electron charge x 6.2425E+20 electron charge = coulomb x 1.60193E-19

coulomb = faraday x 0.01439 faraday = coulomb x 96.480

coulomb = ampere hours x 2.77778E-4 ampere hours = coulomb x 3600

temperature

o o o o K = C + 273.16 C = K - 273.16 o o C = ( F - 32) * 5/9

o o o o K = ( F - 32) * 5/9 + 273.16 F = ( K - 273.16) x 1.8 + 32.0 o o F = C * 9/5 + 32

angle

radian = second(angular) x 4.84814E-6 second(angular) = radian x 0.20626E+6

radian = minute(angular) x 0.000290888 minute(angular) = radian x 3437.75

radian = degree(angular) x 0.017453293 degree(angular) = radian x 57.2957795

radian = revolution x 6.2831853 revolution = radian x 0.159154943

radian = bam x

area

square meter = square centimeter square centimeter = square meter x 1.0E-4 x 10,000

square meter = square inch square inch = square meter x 6.4516E-4 x 1550

square meter = square feet square feet = square meter x 0.09290341 x 10.76387

square meter = square yard square yard = square meter x 0.83613 x 1.19598

square meter = square mile(statute) square mile(statute) = square meter x 2.589998E+6 x 0.368E-6

square meter = acre x 4046.873 acre = square meter x 0.0002471

square meter = circular mil circular mil = square meter x 0.506709E-6 x 1.97352E+6

square meter = hectare x 1.0E+4 hectare = square meter x 1.0E-4

square meter = township x 93.24E+6 township = square meter x 1.0725E-8

square meter = barn x 1.0E-28 barn = square meter x 1.0E+28

volume

cubic meter = cubic centimeter x 1.0E-6 cubic centimeter = cubic meter x 1.0E+6

cubic meter = cubic inch x 0.163871E-4 cubic inch = cubic meter x 61023.74

cubic meter = cubic feet x 0.028317 cubic feet = cubic meter x 35.31466

cubic meter = cubic yard x 0.76456 cubic yard = cubic meter x 1.30795

cubic meter = cubic mile(statute) x cubic mile(statute) = cubic meter x 4.168205E+9 x 0.23991E-9

cubic meter = liter x 0.001 liter = cubic meter x 1000

cubic meter = fluid ounce x 0.295737E-4 fluid ounce = cubic meter x 0.33814E+7

cubic meter = cup x 0.236589E-3 cup = cubic meter x 42267

cubic meter = pint(liquid) pint(liquid) = cubic meter x 21113.4 x 0.4731798E-3

cubic meter = quart(liquid) quart(liquid) = cubic meter x 9.4625E-4 x 1056.8

cubic meter = gallon x 0.003785 gallon = cubic meter x 264.2

cubic meter = barrel x 6.28981 barrel = cubic meter x 0.1589873

cubic meter = pint(dry) x 5.50625E-4 pint(dry) = cubic meter x 1816.118

cubic meter = quart(dry) x 2.75313E-4 quart(dry) = cubic meter x 908.059 quart(dry) = pint(dry) x 0.5

cubic meter = peck x 8.81E-3 peck = cubic meter x 113.507 peck = quart(dry) x 0.125

cubic meter = bushel x 0.03524 bushel = cubic meter x 28.3768 bushel = peck x 0.25

cubic meter = keg x (less than 10 gal)

cubic meter = cord x 3.625

barrel = gallon x 31.5 (food) x 42 (petroleum)

velocity

meter per second = centimeters per second x 100.0

meter per second = kilometer per hour x 0.001

meter per second = inches per second x 39.37

meter per second = feet per second x 3.28083

meter per second = miles per second x 17322.6

meter per second = inches per minute x 0.6562

meter per second = feet per minute x 0.05468

meter per second = miles per hour x 2.2369

meter per second = knots x 1.9438

acceleration

meter per second squared = centimeter per second squared x 100.0

meter per second squared = feet per second squared x 3.28083

meter per second squared = miles per hour squared x 2.2369

force

newton = dyne x 1.0E-5 dyne = newton x 1.0E5

newton = poundal x 7.233 poundal = newton x 0.138

newton = pound force x 7.233/32.17 g pound force = newton X 1/0.2248 x 0.2248

energy

joule = watt second watt = joule per second

joule = erg x 1.0E-7 erg = joule / 1.0E-7

joule = gram calorie x 0.238889E-6

joule = calorie x 1/0.238889 calorie = joule x 0.239

joule = foot pounds x 1.356 foot pounds = joule x 0.7376

joule = kilowatt hour x 3.6E+6 kilowatt hour = joule/(60*60*1000)

joule = watt hour x 1/0.0027 watt hour = joule x 0.00027

joule = horsepower hours x 2.684E+6

joule = BTU x 1/0.00094 BTU = joule x 0.00094

joule = therm x 1/9.478E-9 therm = joule x 9.478E-9

power

watt = volt ampere x 1

watt = calorie per second x 1/0.2390 calorie per second = watt x 0.2390

watt = joule per hour x 1/3600 joule per hour = watt x 3600

watt = erg per second x E-7 erg per second = joule x E+7

watt = kilogram calorie per second x

watt = kilogram calorie per minute x

watt = horsepower(mechanical) x 1/745.705

watt = horsepower(electrical) x 1/760 horsepower(electrical) = watt x 760

watt = horsepower(metric) 1.014 ?

watt = horsepower(boiler) x 9.804E+3 33,520 Btu per hour

watt = B.t.u per minute x 17.57

watt = B.t.u per hour x 17.57*60

watt = foot pound per minute x 0.2260E-3 33000 HP

watt = foot pound per second x 1.356 550 HP

density

kilogram per cubic meter = pound per cubic foot x 16.018 ?

pressure

pascal = newton per square meter x 1

pascal = Kg force per square meter x 1/0.10197

pascal = pound force per square foot x 1/0.020885

pascal = pound force per square inch x 1/0.145038E-3

pascal = ton per square foot x 10.4E-6

pascal = atmosphere(standard) x 1E-5

pascal = inch of water x 0.004

pascal = inches of mercury x 1/0.296E-3

pascal = millimeters of mercury x 0.0075

pascal = bar x 1/1.0E-5 bar = pascal x 1.0E-5

pascal = millibar x 1/0.01 millibar = pascal x 0.01

pascal = torr x 0.0075

torque

newton meter = foot pound x

flow rate

cubic meter per second = gallon per minute x 0.6309E-8

cubic meter per second = cubic feet per minute x 0.4719E-3

specific heat, entropy

o ojoule per kilogram K = B.t.u. per pound F x 4.187E+3

dynamic viscosity

poise = dyne second per square centimeter

kinematic viscosity

stoke = square centimeter per second

electric current

ampere = abampere x 10

ampere = statampere x 0.333333E-9 magnetic flux B

magnetic induction

magnetomotive force

magnetic field strength H

dielectric constant

permittivity constant

rotation rate

radians per second = revolutions per second x

radians per second = revolutions per minute x

PHYSICAL CONSTANTS

There are a number of physical constants that are used in equations

to solve problems in physics. Errors may occur because the dimensionality

and/or units of the physical constant are not known. The table below

presents some physical constants with their typical symbol, dimension,

nominal value and unit of measure in the MKS system.

PHYSICAL CONSTANT SYMBOL DIMENSION MKS VALUE UNIT_________________ ______ _________ _________ ____

3 3air density, normal rho M/L 1.293 Kg/m conditions

air molecule, mass m M 4.81E-26 Kg a

air molecule, w M 0.028952 Kg/mole kilogram molecular weight

2 2atmospheric pressure A M/LT 1.01325 newton/m

Avogadro's number N none 6.023E+23 molecules in molecules in a mole a mole based on 12g of carbon-12

2 2 oBoltzmann's constant k ML /T K 1.380E-23 joule/ K same units as entropy

2 2 electron volt e ML /T 1.60210E-10 joule

3 2 2 2 2electrostatic constant k ML /T Q 8.987E+9 nt m/coulomb reciprocal permittivity m/farad

elementary charge e Q 1.6021892E-19 coulomb

electron mass m M 9.1066E-31 Kg e

faraday f L/T 9.648456E+4 coulomb/mole

2 2 ogas constant of a mole R ML /T K 8.3144 joule/ KAvogadro * Boltzmann

2 2gravity (earth) g L/T 9.80665 m/sec

hydrogen atom mass m M 1.6734E-27 Kg h

hydrogen atom w M 1.0079E-3 Kg/mole kilogram atomic weight

2 2 impedance of free space Z ML /TQ 120Pi ohm 0

mechanical equivalent J none 4186.05 joule/ of heat Kg calorie

2 2 3 permittivity (vacuum) epsi T Q /ML 8.854E-12 farad/meter 0

2 permeability (vacuum) mu ML/Q 4Pi E-7 henry/meter 0

Pi, ratio of circumference Pi none 3.14159265 radians to diameter

2 Planck's constant h ML /T 6.624E-34 joule second

speed of light (vacuum) c L/T 2.99792458E+8 meter/second

speed of sound (air) s L/T 331.45 meter/second

2 2 2 2universal gravitational G L /MT 6.6720E-12 nt m /Kg constant

3 3density of fresh water rho M/L 1000.0 Kg/m definition 62.43 lb/cu-ft 3 3density of sea water rho M/L 1025.0 Kg/m approx 64.00 lb/cu-ft

Note: some constants are related to combinations of other constants : electrostatic constant = 1/ 4Pi permittivity (vacuum) speed of light = 1/ sqrt( permittivity x permeability ) impedance of free space Z = sqrt( permeability / permittivity ) 0

PHYSICS EQUATIONS

SOME EQUATIONS OF PHYSICS

F = m a force equals mass times acceleration, Newton's second law of motion

2 F = m v /r force equals mass times velocity squared over radius, centripetal force of a mass traveling in a circle

2 F = G m m /s gravitational force between mass and mass at distance s 1 2 1 2 with universal gravitational constant G

2g = G m /r acceleration due to gravity on earth earth earth

2 F = k Q Q /s electrical force between charge and charge at distance s 1 2 1 2 with electrostatic constant k . If there is a dielectric then multiply by the non dimensional dielectric constant.

F = 1/2Pi mu I I /s 1 2 electrical force between two parallel wires carrying currents I and I with a spacing s with permeability 1 2 mu. This is the force for one meter of wire length.

2 F = B H s electrical force in a magnetic field equals the magnetic flux times the magnetic intensity applied to an area

2 F = E D s electrical force in an electric field equals the electric field intensity times the electric displacement applied

to an area

s = v t distance equals velocity times time (linear)

v = a t velocity equals acceleration times time (linear)

2s = s + v t + 1/2 a t 0 0 linear distance equals initial distance plus initial velocity times time plus one half acceleration times time squared

2 v = sqrt( v + 2as) f 0 the final velocity equals the square root of the initial velocity squared plus two times the acceleration times the distance traveled

v = sqrt( s g ) the critical velocity for any object to orbit at a c distance s from the source of gravitational field g

vf1 = ((m1-m2)/(m1+m2))*v1 + ((2*m2)/(m1+m2))*v2vf2 = ((m2-m1)/(m1+m2))*v2 + ((2*m1)/(m1+m2))*v1 final velocities of an elastic collision of body with mass m1 and velocity v1 hitting a body with mass m2 and velocity v2. Kinetic energy conserved.

vf = (m1*v1 +m2*v2)/(m1+m2) final velocity of an inelastic collision of body with mass m1 and velocity v1 hitting and sticking to a body with mass m2 and velocity v2. Kinetic energy is not conserved but is converted.

theta = omega t angle equals angular velocity times time (rotational)

omega = alpha t angular velocity equals angular acceleration times time (rotational)

2theta = theta + omega t + 1/2 alpha t 0 0

angular rotation equals initial angle plus initial angular velocity times time plus one half angular acceleration times time squared

2 w = sqrt(w + 2 alpha * angle) f 0 the final angular velocity equals the square root of the initial angular velocity squared time twice the angular acceleration times the angle traveled

2I = mass*radius moment of inertia, about an axis, integral from 0 to mass of radius squared times incremental mass

T = I alpha torque equals moment of inertia times angular acceleration

L = I omega angular momentum equals moment of inertia times angular velocity

2E = 1/2 I omega kinetic energy equals one half moment of inertia times angular velocity squared

P = I alpha omega power equals moment of inertia times angular acceleration times angular velocity

W = I alpha theta work equals moment of inertia times angular acceleration times angle traveled

E = I R voltage equals current through a resistor times the resistance

I = C (E - E )/(t - t ) 2 1 2 1 the current through a capacitor equals the capacitance times the change in voltage over the change in time

E = I * time / C actually an integral of current divided by C one amp for one scecond charges one farad to one volt

E = L (I - I )/(t - t ) 2 1 2 1 the voltage across an inductor equals the inductance times the change in current over the change in time

I = E * time / L actually a derivative of voltage divided by L one volt change in one second causes a current of one amp in a 1 henry inductor

C = epsi A/s the capacitance in farad of a parallel plate capacitor equals the permittivity times the area divided by the spacing.

L = n mu r (ln 8r/d - 7/4) the inductance in henry of n turns of wire with diameter d closely wrapped in a coil of radius r with permeability mu is approximately given by this equation.

H = 1/2 I / r the magnetic intensity at the center of a current loop equals 1/2 the current divided by the radius of the loop

B = mu H the magnetic flux equals the permeability times the magnetic intensity

D = epsi E the electric displacement equals the permittivity times the electric field intensity

P = E I power equals an electrical potential causing a current

P = F s power equals a force applied over a distance

2 E = m c energy from converting a mass to energy ( c = speed of light)

E = I omega energy of rotation, Inertia times rotational velocity

2 E = 1/2 m v kinetic energy of a mass traveling at a velocity

E = m g s potential energy of a mass in a gravitational field at a height s

E = 1/2 B H V energy of a magnetic field in the volume V with magnetic flux B and magnetic intensity H. This is usually an integral of an incremental volume times B times H in the incremental volume.

E = 1/2 D E V energy of an electric field in the volume V with electric displacement D and electric field intensity E. This is usually an integral of an incremental volume times D times E in the incremental volume.

2E = 1/2 C V energy stored in a capacitor with capacitance C having

a voltage V

2E = 1/2 L I energy stored in an inductor with inductance L having a current I

T = F s torque equals the force applied at radius s

T = I alpha torque equals the rotational inertia times the angular acceleration

2E = P V = R T = Na k T = 1/3 N m v ideal gas law rms These relations are for one mole (kilogram molecule) of an ideal gas at an absolute pressure P, volume V, gas constant R, Avogadro's number Na, Boltzmann's constant k, temperature T in Kelvin, gas molecule mass m, root mean square speed of the molecules v in meters per second. Each section of the equation rms represents energy in joule. P V = n R T for n moles of the gas. With sigma being density, P = sigma R T / M where M = mass/n

2 2P + 1/2 rho v + rho g z = P + 1/2 rho v + rho g z 1 1 1 2 2 2

This equation relates pressure P, velocity v and relative height z for a non compressible fluid in a pipe, observed at location 1 and location 2. rho is the density of the fluid and g is the gravitational constant.

2L = C rho v A / 2 L the lift force equals the dimensionless coefficient of lift times the air density times the velocity squared times the surface area divided by 2.

2D = C rho v A / 2 D the drag force equals the dimensionless coefficient of drag times the air density times the velocity squared times the surface area divided by 2.

nu = mu / rho the kinematic viscosity equals the dynamic viscosity over the density in a fluid

P = Q (p - p ) 1 2 the power, P, required to drive a volume rate of flow, Q, from pressure p to pressure p . 1 1o o C = K - 273.16 degrees centigrade equals Kelvin minus 273.16

o o F = ( K -273.16) x 9/5 + 32 degrees Fahrenheit as a function of Kelvin

Go to top

Last updated 5/11/10