# Precalculus : Solve Angular Velocity Problems

## Example Questions

### Example Question #1 : Solve Angular Velocity Problems

If a ball is travelling in a circle of diameter  with velocity , find the angular velocity of the ball.

Explanation:

Using the equation,

where

=angular velocity, =linear velocity, and =radius of the circle.

In this case the radius is 5 (half of the diameter) and linear velocity is 20 m/s.

.

### Example Question #2 : Solve Angular Velocity Problems

Suppose a car tire rotates  times a second. The tire has a diameter of  inches. Find the angular velocity in radians per second.

Explanation:

Write the formula for angular velocity.

The frequency of the tire is 8 revolutions per second. The radius is not used.

Substitute the frequency and solve.

### Example Question #3 : Solve Angular Velocity Problems

What is the angular velocity of a spinning top if it travels  radians in a third of a second?

Explanation:

Write the formula for average velocity.

The units of omega is radians per second.

Substitute the givens and solve for omega.

### Example Question #4 : Solve Angular Velocity Problems

A  diamter tire on a car makes  revolutions per second. Find the angular speed of the car.

Explanation:

Recall that  .

Since the tire revolves 9.3 times/second it would seem that the tire would rotate

or .

We use  to indicate that the tire is rolling 360 degrees or  radians each revolution (as it should).

Thus,

Note that radians is JUST a different way of writing degrees. The higher numbers in the answers above are all measures around the actual linear speed of the tire, not the angular speed.

### Example Question #5 : Solve Angular Velocity Problems

A car wheel of radius 20 inches rotates at 8 revolutions per second on the highway. What is the angular speed of the tire?