Expert answer:Angular and Linear Velocity

Answer & Explanation:Please help me with these questions on Angular and Linear Velocity.See attached document.Angular & Linear Velocity
angular_and_linear_velocity_applications.doc

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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.
•
•
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.
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.
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.
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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