FISIKA DASARBy: Mohammad Faizun, S.T., M.Eng.

Head of Manufacture System LaboratoryMechanical Engineering Department

Universitas Islam Indonesia

1. QUANTITY (besaran) and UNITS (satuan)

• From the picture below you can exactly say that line B is longer than line A. Paper D is narrower than paper C.

• Length and Area are two examples of quantity. Quantity is the properties of matter which can be measured.

A

B

C D

Everything which can be MEASURED

is quantity.

No Phenomena Can be measured? How? Is it quantity?1 Time2 Age3 Mass4 Temperature5 Emotion6 Color7 Length8 Line9 Bright

10 Love

Fill in the empty cell on the table below!

“Everything that can be COUNTED is quantity”. Is

this statement true? Why?What is the difference between COUNTING

(menghitung) and MEASURING (mengukur)?

• We can differentiate two things or more by comparing their quantities for example: longer, narrower, lighter, colder, etc. But you still confused unless you tell exactly how big the quantities. So we need units.

• For example:1. 12 cm, 30 feet, 120 km. cm, feet, and km are

examples of units for length quantity.2. 12 gram, 30 pounds, 2 ton. Gram, pound, and

ton are examples of units for mass quantity.3. 5 second, second is an example of units for

time.

Quantity without units is worthless.

• Determine the quantity and the units in each information below if possible!

1. Ruddy is 1.75 meters tall.2. Mr. Anton has five cars.3. The mass of the book is 1 kg.4. We need 4 litres of water a day.5. I will stay here a month.6. The speed of the car is 100 km/h.

QUANTITY (besaran) UNITS

(satuan)

MEASUREMENT(Pengukuran)

RESULTValue + unit

6 cm

Satuan adalah nilai tertentu yang

disepakati dari suatu besaran.

Pengukuran: membandingkan nilai

besaran dengan satuannya.

• There are two kinds of units: SI (Systéme International) units and non SI units.

• SI units is Internationally accepted, means all people in all countries know that units.

Units

Non SI Units

SI Units

m k s

c g s

(gaussian)

No QuantitySI

Non SImks cgs

1 Length meter centimeter inchi, feet, mil

2 Mass kilogram gram pound, ton, ons

3 Time second second second4 Volume m3 cm3 liter, galon5 Density kg/m3 g/cm3 kg/l, g/l, pound/l

No QuantitySI

Non SImks cgs

1 Length meter centimeter inchi, feet, mil

2 Mass kilogram gram pound, ton, ons

3 Time second second second4 Volume m3 cm3 liter, galon5 Density kg/m3 g/cm3 kg/l, g/l, pound/l

• It’s suggested to always use SI units. How are those SI units defined?

• one meter

In October 1983, the meter (1 m) was redefined as the distance traveled by light in vacuum during a time of 1/299 792 458 second. In effect, this latest definition establishes that the speed of light in vacuum is precisely 299 792 458 m per second. One meter that we use today is same with the definition. We use roll meter for example to measure length of the wood bar or others.

• one kilogram

Mass is amount of matter in an object. To get better understanding please compare two cans filled in with different amount of marbles. Guess which can has more weight!

Can A has marbles less than can B, 8 less than 16, right? So, can A has smaller mass than can B. The basic SI unit of mass, the kilogram (kg), is defined as the mass of a specific platinum–iridium alloy cylinder kept at the International Bureau of Weights and Measures at Sèvres, France. This mass standard was established in 1887 and has not been changed since that time because platinum–iridium is an unusually stable alloy (Fig. 1.5). We use arm balance to measure mass of something.

AB

One Kilogram Standard Arm Balance

Benarkah neraca pegas bisa dipakai untuk menghitung massa sebuah benda dimana saja? Jelaskan alasannya!

• one second

The basic SI unit of time, the second (s), is defined as 9,192, 631,770 times the period of vibration of radiation from the cesium-133 atom.

• In addition to the basic SI units of meter, kilogram, and second, we can also use other units, such as millimeters and nanoseconds, where the prefixes milli- and nano- denote various powers of ten.

2. BASIC QUANTITIES (besaran pokok) and ITS DERIVATION (besaran turunan)

• Fundamentals or basic quantities is now believed as quantities that not derived from other quantities. Even they form other quantities.

NO Quantity SI Units Symbol Dimensions Non SI

1 Mass kilogram kg [M] Pound, ons, etc

2 Length meter m [L] Inchi, feet

3 Time second s [T]

4 Electric Current ampere A [I]

5 Temperature kelvin K [θ] Rankine, Fahrenheit

6 Luminous Intensity candela cd [Cd]

7 Amount of Substance mole mole [mole]

8 Angle 2D radian rad

9 Angle 3D steradian sr

Besaran turunan

• Besaran turunan adalah besaran yang terbentuk dari besaran-besaran pokok.

• Contoh: Luas panjang x panjang,Volume panjang x panjang x panjangBerat massa x panjang x waktu-2

Volume: 10 cm x 10 cm x 10 cm. : 1000 cm3.

10 cm

10 cm

10 cm

Contoh besaran turunan

SCALAR AND VECTOR QUANTITIES

Quantities

Basic

derivative

scalar

vector

Scalar quantity is one that has only value but no direction. Example: mass, length, time. All basic quantities are scalar quantities.Vector quantity is one that has both value and direction. Example: force, velocity, pressure, etc.

See figure below!

A. You know that the volume of cylinder is 1 liter. If you asked where is the direction of that volume you will not be able to answer, because volume doesn’t have direction. So, volume is scalar quantities.

B shows that the velocity of the block is 10 m/s and the direction is rightward. Having velocity without direction is impossible.

AB

1 L

v = 10m/s

QUESTIONS 1. What is the definitions of quantity?2. Please fill in the table below!

No TERM Quantity? True or Not True

a Mass Yesb Volume Yesc Area Nod Weight Yese Atoms number Yesf Force Yesg Height Yesh Color Noi Taste Yesj Sound volume No

3. Is it true that quantity has two kinds, SI and non SI?4. Suppose that two quantities A and B have different

dimensions. Determine which of the following arithmetic operations could be physically meaningful: (a) A-B (b) A/B (c) B+A (d) AB.

5. What are use of units?6. Mention the differences between basic units and derived

units!7. Why are units very important for us?8. Fill in the table below.

No UNITS SI or Non SI mks or cgsa milb kmc cm3

d grame onsf decigramg secondh milisecondi yardj liter

No QUANTITIES Basic or Not Units Scalar or Vector

a Lengthb Massc Densityd Forcee Electric Chargef Flowrate of Water g Velocityh Energyi Powerj Year

3. DIMENSIONAL ANALYSIS

• The word dimension has a special meaning in physics. It usually denotes the physical nature of a quantity. Whether a distance is measured in the length unit feet or the length unit meters, it is still.

• For example we will find the dimension for volume (V).

= [L] x [L] x [L} = [L]3

So the dimension of volume is [L]3.

thicknesswidthlengthV

mmmm 3

No Quantity Units Dimension

1 Area m2 [L]2

2 Speed m/s [L][T]-1

3 Acceleration m/s2 [L][T]-2

4 Density kg/m3 [M][L]-3

5 Force kg m/s2 [M][L][T]-1

Example• Suppose we are told that the acceleration a of a particle

moving with uniform speed v in a circle of radius r is proportional to some power of r, say rn, and some power of v, say vm. How can we determine the values of n and m?

• SolutionLet us take a to be where k is a dimensionless constant of proportionality. Knowing the dimensions of a, r, and v, we see that the dimensional equation must be

mnvkra

2TL mn

TLL )(

2TL

m

mn

TL

This dimensional equation is balanced under the conditions

n + m = 1 m = 2 So, n = -1

Then we can write the acceleration expression as

mnvkra 21 vrka

rvka

2

(in the next discussion about uniform circular motion we will see this formula)

Exercise:

Please find the dimension of:

a. Gravity (g) f. electrical force.b. Heat energy g. Powerc. Pressure h. Electrical charged. Electrical resistance i. Capacitance of

Capacitore. Spring constant (k) j. electron mass.

About the Author– Name : Mohammad Faizun, S.T., M.Eng.– Education : B.Eng., Gadjah Mada University (2003-

2007): M.Eng., University of Malaya (2009-2011).

– Job : a. Production Engineer, Bekaert Stanwick (2007- 2009)

b. Head of Manufacture System Laboratory, Islamic University of Indonesia (2011- now)

c. Lecturer at Mechanical Engineering Dep. Islamic University of Indonesia (2011- now)

– Expertise : Robotics, Electronics, Microcontroller, PLC, Computer Vision and Image Processing,

and C++ Programming.