What you will learn

How to find linear and angular velocity
1
Angular Displacement
2
Imagine putting a “dot” on the outside edge of a CD. Now
spin the CD counterclockwise. The change in angle from
the starting position as the “dot” moves around the CD is
called “angular displacement”.
Each revolution equals 2pi radians.
Objective: 6-2 Linear and Angular Velocity
Calculating Angular Displacement
3

Determine the angular displacement in radians of
4.5 revolutions. Round to the nearest tenth.
You try: Determine the angular displacement in
radians of 8.7 revolutions. Round to the nearest
tenth.
Objective: 6-2 Linear and Angular Velocity
Angular Velocity
4
The ratio of change of the central angle to the time
required for the change is known as “angular velocity”.
Kind of like rate = distance/time except the “distance” is the
degrees of change.
The formula to calculate angular velocity is:



t
 is the Greek letter “omega”
Objective: 6-2 Linear and Angular Velocity
Example
5
Determine the angular velocity if 7.3 revolutions are
completed in 5 seconds. Round to the nearest tenth.
Step 1: Convert 7.3 revolutions to radians

Step 2: Plug in!
Objective: 6-2 Linear and Angular Velocity
You Try
6

Determine the angular velocity if 5.8 revolutions are
completed in 9 seconds. Round to the nearest tenth.
Objective: 6-2 Linear and Angular Velocity
Linear Velocity
7


The rate at which something (like our dot on the cd
example) moves around a circle is called linear
velocity.
Once again, it is kind of like rate = distance/time
but the distance in this case is the “distance” around
a circle (arc length).
Objective: 6-2 Linear and Angular Velocity
Dimensional Analysis
8


Sometimes you need to do some unit conversions in order to solve
some of these problems.
Example: A circular serving table in a buffet has a radius of 3 feet. It
makes 2.5 revolutions per minute. Determine the angular velocity in
radians per second of something sitting on the table.
2.5 revolutions
1 minute
x
1 minute
60 seconds
Objective: 6-2 Linear and Angular Velocity
x
radians
2
1 revolution
The Formula
9

You can kind of “derive” the formula for linear
velocity.
What is the formula for arc length?

What do we need to divide by?

Objective: 6-2 Linear and Angular Velocity
THE Formula
10

If an object moves along a circle of radius of r units, then
its linear velocity “v” if given by:
vr


t
or
What do the “parts” stand for?
Objective: 6-2 Linear and Angular Velocity
v  r
An Example
11

Determine the linear velocity of a point rotating at an
angular velocity of 17 radians per second at a distance
of 5 centimeters from the center of the rotating object.
Round to the nearest tenth.
Objective: 6-2 Linear and Angular Velocity
You Try
12

Determine the linear velocity of a point rotating at an
angular velocity of 31 radians per second at a
distance of 15 cm from the center of the rotating object.
Round your answer to the nearest tenth.
Objective: 6-2 Linear and Angular Velocity
A Word Problem…Oh Boy!
13

The tires on a race car have a diameter of 30
inches. If the tires are turning at a rate of 2000
revolutions per minute, determine the race car’s
speed in miles per hour.
Objective: 6-2 Linear and Angular Velocity
Homework
14

page 355, 13-33 odds, 34
Objective: 6-2 Linear and Angular Velocity