Vector, Scalar and Units Review

Vector vs. Scalar

Definitions: Vectors are any quantity in physics that can

be characterized by both its magnitude and direction.

Scalars are any quantity in physics that can be characterized by magnitude only.

What is Magnitude?

To keep is simple, magnitude can be thought of the value associated with a vector or scalar quantity. Ex. A boy runs 100 meters in the northerly

direction in 20 seconds. What is the magnitude of his average velocity?

Ans.

Note: magnitude is the value 5 m/s, which is also the scalar component of the velocity vector. In this example, it is the speed.

sms

m

t

dv /5

20

100

d

Stands for? Displacement or distance

The Units are? meters (m)

Displacement is a vector quantity. Distance is a scalar quantity.

v

Stands for? Velocity or speed

The Units are? meters per second (m/s)

Velocity is a vector quantity. Speed is a scalar quantity, and is the

magnitude of the velocity vector.

a, ac

Stands for? Acceleration ac represents centripetal acceleration, which is

an inward directed acceleration that applies to objects moving in circular paths.

The Units are? meters per second2 (m/s2)

Acceleration is a vector quantity.

m

Stands for? mass

The Units are? kilograms (kg)

Mass is a scalar quantity.

t

Stands for? time

The Units are? seconds (s)

Time is a scalar quantity.

F, Fg, Fe

Stands for? Force Fg = mg, is the force due to gravity or weight.

Fe is an electrostatic force.

The Units are? Newtons (N)

Force is a vector quantity

p

Stands for? Momentum = mv

The Units are? Kilogram-meter per second (kgm/s)

momentum is a vector quantity.

J

Stands for? Impulse = Ft

The Units are? Newton-second (Ns)

Impulse is a vector quantity.

r

Stands for? Radial distance between two points or objects.

The Units are? meters (m)

r is a scalar quantity

E

Stands for? Electric Field Intensity or Strength.

The Units are? N/C (F/q) V/m (V/d)

Electric Field Intensity is a vector quantity.

q

Stands for? Charge

Units are? Coulombs (C)

Alternate symbol representation: Q or e

Charge is a scalar quantity.

I

Stands for? Current (Flow of positive charge).

Units are? Amperes (A)

Current is a scalar quantity

V

Stands for? Volts / Voltage / Potential Difference / Electric

Potential The Units are?

Volts Electric Potential is a scalar quantity.

R

Stands for? Resistance (An electrical property of a

material that is a measure of the resistance to flow of electrons in relation to an electrical potential.)

The Units are? Ohms (Ω)

Resistance is a scalar quantity.

Stands for? Resistivity (A natural property of a material

that is a measure of the resistance to the flow of electrons.)

The Units are? Ωm

A

Stands for? Cross-sectional area (of a conductor).

The Units are? m2

L

Stands for? Length (of a conductor).

The Units are? m

E

May also be represented by U or W Stands for?

Energy The Units are?

Joules (J) Energy is a scalar quantity.

W

Stands for? Work

The Units are? Joules (J)

Work is a scalar quantity.

P

Stands for? Power

The Units are? Watts (W) Joule per second (J/s)

Power is a scalar quantity.

B

Stands for? Magnetic Field Intensity.

The Units are? Tesla (T)

Magnetic Field Intensity is a vector quantity.

c

Stands for? Speed of light

The Units are? m/s

The Value is? 3.0 x 108 m/s

f

Stands for? Frequency (The number of waves that pass a

point in space per unit of time.) The Units are?

Hertz (Hz), cycles/second, or (1/s) Frequency is a scalar quantity.

T

Stands for? Period (The time required for a wave to

complete 1 cycle, or one wavelength.) The Units are?

Seconds (s) The period is a scalar quantity.

λ

Stands for? Wavelength (The distance at which a wave will

repeat the same pattern over again.) The Units are?

Meters (m) Wavelength is a scalar quantity

n

Stands for? Index of refraction (property of a material that

is used to determine both the speed of light in that material and the amount that the light will bend.)

Quantum energy level. The Units are?

None

θi, θr, θ1, θ2

Stands for? Angle of incidence (θi)

Angle of reflection (θr)

Angle of incidence (θ1)

Angle of refraction (θ2) All angles are relative to a normal to the surface.

h

Stands for? Planck's Constant

The Units are? Joule • second (J.s)

The value is: 6.626 x 10-34 J.s

k

Stands for? Electrostatic constant

The Units are? Newtons • meters2 / Coulombs2 (Nm2/C2)

The Value is: 8.99 x 109 Nm2/C2

e

Stands for? Elementary charge Charge on a proton or electron

The Units are? Coulombs (C)

The Value is: 1.6 x 10-19 C

Kinematics

Name Symbol Unit Name Symbol

Distance / Displacement d meters m

Time t seconds s

Velocity / Speed v meters / second m/s

Acceleration a meters / second2 m/s2

Forces

Name Symbol Unit Name Symbol

Force F Newton N (kg·m/s2)

Net Force Fnet = ma Newton N (kg·m/s2)

Normal Force FN or N Newton N (kg·m/s2)

Tensional Force FT or T Newton N (kg·m/s2)

Weight / Gravitational Force Fg or W = mg Newton N (kg·m/s2)

Friction Ff Newton N (kg·m/s2)

Centripetal Force Fc = mv2/r Newton N (kg·m/s2)

Coefficient of Friction

Work & Energy

Name Symbol Unit Name Symbol

Work W = Fd Joule or Newton - meter J or Nm

Potential Energy PE Joule J

Kinetic Energy KE = ½mv2 Joule J

Internal Energy / Heat Q Joule J

Power P Watt W or J/s

Momentum P = mv Kilogram-meter/second kg∙m/s

Impulse J = Ft Newton-second N∙s

Spring Constant k Newton/meter N/m or kg/s2

Electrostatics

Name Symbol Unit Name Symbol

Electrostatic Force Fe Newton N

Electric Field Intensity E Newtons/CoulombVolts/Meter

N/CV/m

Charge Q, q Coulombs C

Current Electricity

Name Symbol Unit Name Symbol

Current I Amperes A

Voltage / Potential Difference / Electric Potent.

V Volts V

Resistance R Ohms

Resistivity Ohm – meter m

Cross-sectional Area A Meters2 m2

Length L Meters m

Power P WattsJoules/second

WJ/s

Energy E Joules J

Work W Joules J

Magnetism

Name Symbol Unit Name Symbol

Magnetic Field Intensity B Tesla T

Waves

Name Symbol Unit Name Symbol

Speed v Meters/second m/s

Speed of Light c Meters/second m/s

Wavelength Meters m

Frequency f Hertz (Hz)1/seconds

1/s

Period T Time (seconds) s

Light & Optics

Name Symbol Unit Name Symbol

Index of Refraction n None

Angle of Incidence i, or 1 Degrees / Radians o, Rad

Angle of Reflection r Degrees / Radians o, Rad

Angle of Refraction 2 Degrees / Radians o, Rad

Constants

Name Symbol Unit Name Symbol

Planck’s Constant h 6.626 E-34 J.s

Electrostatic Constant k 8.99 E9 N.m2/C2

The elementary Charge e 1.6 E-19 C

Vector or Scalar?

Scalars Vectors

Distance Power Displacement Momentum

Speed Charge Velocity Impulse

Mass Current Acceleration Electric Field StrengthTime Voltage Force

Work Resistance Weight Magnetic Field StrengthEnergy Wavelength Normal Force

Kinetic Energy Frequency Tension

Pot. Energy Period Friction

Elect. Energy Centripetal ForceInternal Energy