1. What you will learn
How to find linear and angular velocity

2. Angular Displacement
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

3. Calculating Angular Displacement
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

4. Angular Velocity
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:
is the Greek letter “omega”
Objective: 6-2 Linear and Angular Velocity

5. Example
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

6. You Try
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

7. Linear Velocity
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

8. Dimensional Analysis
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 x 1 minute x radians
1 minute 60 seconds 1 revolution
Objective: 6-2 Linear and Angular Velocity

9. The Formula 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

10. THE Formula
If an object moves along a circle of radius of r units, then its linear velocity “v” if given by: or
What do the “parts” stand for?
Objective: 6-2 Linear and Angular Velocity

11. An Example
Determine the linear velocity of a point rotating at an angular velocity of 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

12. You Try
Determine the linear velocity of a point rotating at an angular velocity of 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

13. A Word Problem…Oh Boy!
The tires on a race car have a diameter of 30 inches. If the tires are turning at a rate of revolutions per minute, determine the race car’s speed in miles per hour.
Objective: 6-2 Linear and Angular Velocity

14. Homework
page 355, odds, 34
Objective: 6-2 Linear and Angular Velocity