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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

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
scalars
Scalars

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

vectors
Vectors

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
slide7
Vector
  • 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.

B

A

C

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

A

C

B

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

y

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.

R

Ry

q

x

Rx

resolving a vector into components
Resolving a vector into components

y

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

Rx = Rcos(q)

Ry = Rsin(q)

tan q = Ry / Rx

R = √(Rx2 + Ry2)

R

Ry

q

x

Rx

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
summary
Summary
  • 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.
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