Precalculus : Solve Angular Velocity Problems

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Angular And Linear Velocity

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

Possible Answers:

Correct answer:

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 : Angular And Linear Velocity

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

Possible Answers:

Correct answer:

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 #2 : Angular And Linear Velocity

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

Possible Answers:

Correct answer:

Explanation:

Write the formula for average velocity.

The units of omega is radians per second.

Substitute the givens and solve for omega.

Example Question #3 : Angular And Linear Velocity

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

Possible Answers:

Correct answer:

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, 

 is your final answer.

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 #3 : Angular And Linear Velocity

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

Possible Answers:

None of these.

Correct answer:

Explanation:

Angular speed is the same as linear speed, but instead of distance per unit time we use degrees or radians. Any object traveling has both linear and angular speed (though objects only have angular speed when they are rotating).

Since our tire completes 8 revolutions per second we multiply by  since a full rotation (360°) equals .

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