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TOPIC 2. Physical Quantities: Scalar and Vector Quantities. Lecture Outline. Scalar Quantities Vector Quantities Addition of Vector Quantities Application of Vector Quantities. Lecture Objectives. After this lecture, students will be able: To define scalar quantities

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Topic 2


Physical Quantities: Scalar and Vector Quantities

Lecture outline
Lecture Outline

  • Scalar Quantities

  • Vector Quantities

  • Addition of Vector Quantities

  • Application of Vector Quantities

Lecture objectives
Lecture Objectives

  • After this lecture, students will be able:

    • To define scalar quantities

    • To define vector quantities

    • To analyze vector addition using graphical approach

    • To analyze vector addition using vector components


Scalar quantities are those which are described solely by their magnitudeSome examples are:

Mass e.g. 14 [kg], 36 [lbs], …

Time e.g. 10 seconds, 40 minutes, …

Volume e.g. 1000 cm3, 4 litres, 12 gallons

Temperature e.g 14 oF , 25 oC, …

Voltage e.g. 9 Volts, etc


Vector quantities are those which need to be described by BOTH magnitude and direction

Some of the most common examples which we will encounter are:

Velocity e.g. 100 [mi/hr] NORTH

Acceleration e.g. 10 [m/sec2] at 35o with respect to EAST

Force e.g. 980 [Newtons] straight down (270o)

Momentum e.g. 200 [kg m/sec] at 90o.

Vectors recall
Vectors recall

  • Quantities with magnitude and direction

  • Magnitude

    • Size or quantity in unit of measurement

    • 10 meters, 5 Newtons

  • Direction

    • Compass direction: North, Southeast

    • Angle: 25o from the positive x axis

  • Examples

    • Distance—5 miles North

    • Acceleration—10m/s2 down

    • Force—100 Newton at an angle of 30o above the horizontal

Topic 2


  • an arrow drawn to scale used to represent a vector quantity

  • vector notation

Ways to add vectors
Ways to add vectors

  • Graphically

    • Tip to tail method

    • Parallelogram

  • Using components

Graphical addition of vectors
Graphical addition of vectors

Arrange tail of vector B on tip of vector A. The vector sum C, called the resultant, is drawn from the tail of vector A to the tip of vector B. The order of addition does not matter.




C = A + B

Tip to tail method
Tip-to-Tail Method

  • Example 1: Add these vectors using the tip-to-tail method.


Parallelogram method
Parallelogram Method




B (parallel)

Note: B has direction and size, but starting point is arbitrary

Subtraction and multiplication of vector
Subtraction and Multiplication of Vector

1. The negative of a vector is a vector of the same magnitude but in the opposite direction. Thus vector v = 5 m/s due east, then –v = 5 m/s due west.

2. In order to subtract one vector from another, rewrite the problem s that the rules of vector addition can be applied.

Example :

A – B can be written as A + (-B)

Vector components
Vector components


A vector R which lies at some angle q to an axis has two perpendicular components, Rxand Ry which lie on the axes.

If you draw a straight line from the tip of vector R to the axis, this distance along the axis is the magnitude of the component.






Resolving a vector into components
Resolving a vector into components


Applying trigonometry, the components of the vector R can be defined.

Rx = Rcos(q)

Ry = Rsin(q)

tan q = Ry / Rx

R = √(Rx2 + Ry2)






Analytical addition of vectors
Analytical addition of vectors

  • To add vectors analytically, add their components

  • Resolve individual vectors to be added into x and y or North and East components using trig

  • Add all of the x components

  • Add all of the y components

  • Find the magnitude of the Resultant (the vector sum) by taking the square root of the sum of the squares of the x and y components

  • Find the angle of the Resultant using trig


  • In nature, there are two types of quantities, scalars and vectors

  • Scalars have only magnitude, whereas vectors have both magnitude and direction.

  • The vectors we learned about are distance, velocity, acceleration, force, and momentum

  • The scalars we learned about are time, and Energy.