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# TOPIC 2 - PowerPoint PPT Presentation

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

• Scalar Quantities

• Vector Quantities

• Application of Vector Quantities

• 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.

• 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

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

• vector notation

• Graphically

• Tip to tail method

• Parallelogram

• Using components

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

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

+

A

C

B

B (parallel)

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

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)

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

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

• 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

B

A

C

B

• 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.