# In your studies you have explored the concepts of angular and linear velocity.

Question

In your studies you have explored the concepts of angular and linear velocity. Angular velocity is the rate of change of the angle of displacement.It is calculated by dividing the angle of displacement by the time. Linear velocity is the rate of change of distance traveled.For the purposes of this activity, linear velocity is defined as the radius of a given circle times the angular velocity.

Use the following formulas:

angular velocity=angular displacement/time

linear velocity=radius x angular velocity

Assignment: Angular and Linear Velocity Applications

Follow the directions to solve each problem that uses bicycle wheels as an application of angular

and linear velocity. Solve the problems in order and use appropriate units. Show all work leading

to your answer. Be sure to include an explanation to describe what the answer means for each

situation.

Use this information to help you:

Bicycles are classified by the diameter of their wheels. For example, a 20-inch bike has wheels

with a 20-inch diameter, and a 26-inch bike has wheels with a 26-inch diameter.

1. The number of times a bicycle tire rotates in a given time period is directly related to the

distance traveled in that time period. Consider the following scenarios.

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A bicycle with 26-inch tires is being pedaled so that the tires are rotating at a rate of 200

revolutions per minute.

A second bicycle with 20-inch tires is being pedaled so that the tires are also rotating at a

rate of 200 revolutions per minute.

Which bicycle do you think is going faster? Why? Use the concepts of angular and linear velocity

in your answer.

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2. Calculate the angular speed of the 26-inch bicycle rotating at 200 revolutions per minute.

Express your answer in radians per minute. Use π = 3.14.

3. Next, calculate the linear speed of the 26-inch bicycle being pedaled at a rate of 200

revolutions per minute. Express your answer in inches per minute rounded to the nearest whole

number. (Hint: The diameter of the wheel is 26 inches.)

4. Expressing a speed in inches per minute has very little meaning in the context of the problem.

It would be more useful to express the answer in miles per hour. Use dimensional analysis

procedures to transform your answer from problem 3 into miles per hour, rounded to the nearest

tenth.

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5. Use your answers to problems 2-4 to calculate the linear speed, in miles per hour, of a 20-inch

bicycle being pedaled at a rate of 200 revolutions per minute.

6. Now that you have calculated the linear speed of both bicycles, look back at your answer to

problem 1. Were you correct about which bicycle was going faster? If so, explain why, using the

results of problems 2-5. If you were not correct, revise your answer to problem 1 in this problem,

using the results of questions 2-5 in your response.

7. Suppose you are riding the 20-inch bike illustrated in this set of problems, and a friend is riding

the 26-inch bike. Assuming that your friend is pedaling the 26-inch bike at a rate of 200

revolutions per minute, will you have to pedal the 20-inch bike faster or slower than 200

revolutions per minute for you and your friend to be riding at the same speed? Explain your

answer in terms of angular and linear velocity.

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8. At what rate would you have to pedal a 20-inch bike so that it traveled at a linear speed of 15.5

miles per hour? Express you answer in revolutions per minute rounded to the nearest whole

number. (Hint: First change miles per hour into inches per minute.)

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