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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.
•
•
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.
© K12 Inc.
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.
© K12 Inc.
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.
© K12 Inc.
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.)
© K12 Inc.
Assignment: Angular and Linear Velocity Applications (40 points)
Total Score:
Student Name:
High Grades (5 points each)
High scoring students will do
the following:
1. Which bike is
faster?
The student selects the bike
that is faster and supports his
or her choice with a complete
explanation that includes
definitions of angular and
linear velocity.
Middle Grades (3-4 points
each)
Middle scoring students will do
the following:
The student selects the bike that
is faster and supports his or her
choice with a partial explanation
that includes definitions of
angular and linear velocity.
Low Grades (1-2 points each)
Low scoring students will do the
following:
Unacceptable (0 points
each)
The student writes a response
that does not directly reference
angular and linear velocity.
The student’s response does
not include a discussion of
angular and linear velocities.
Score:
Comments:
2. 26-inch bike
angular speed
calculations
The student correctly
calculates the angular speed
of the 26-inch bike and shows
appropriate work to support
the answer.
The student incorrectly
calculates the angular speed.
However, he or she shows
sufficient work so that 1-2 minor
errors can be found.
The student correctly calculates
the angular speed. However, the
answer is not supported by
sufficient work.
The student incorrectly
calculates the angular speed
and shows insufficient work
to support the answer.
The student correctly
calculates the linear speed in
inches per minute of the 26inch bike and shows
appropriate work to support
the answer.
The student incorrectly
calculates the linear speed.
However, he or she shows
sufficient work so that 1-2 minor
errors can be found.
The student correctly calculates
the linear speed. However, the
answer is not supported by
sufficient work.
The student incorrectly
calculates the linear speed
and shows insufficient work
to support the answer.
The student correctly
calculates the linear speed in
miles per hour of the 26-inch
The student incorrectly
calculates the linear speed.
However, he or she shows
The student correctly calculates
the linear speed. However, the
answer is not supported by
The student incorrectly
calculates the linear speed
and shows insufficient work
Score:
Comments:
3. 26-inch bike
linear speed inches
per minute
Score:
Comments:
4. 26-inch bike
linear speed miles
per hour
© K12 Inc.
bike and shows appropriate
work to support the answer.
sufficient work so that 1-2 minor
errors can be found.
sufficient work.
to support the answer.
The student correctly
calculates the linear speed in
miles per hour of the 20-inch
bike and shows appropriate
work to support the answer.
The student incorrectly
calculates the linear speed.
However, he or she shows
sufficient work so that 1-2 minor
errors can be found.
The student correctly calculates
the linear speed. However, the
answer is not supported by
sufficient work.
The student incorrectly
calculates the linear speed
and shows insufficient work
to support the answer.
The student revisits and
revises the answer to problem
1. The answer is written in
complete sentences and
references the student’s
answers to problems 2-5.
The student revisits and revises
the answer to problem 1. The
answer references the student’s
answers to problem 2-5.
However, it is not written in
complete sentences.
The student’s response does not
directly reference original
response or the answers to
problems 2-5.
The student’s response does
not reference the original
response or the answers to
problems 2-5 and is not
written in complete
sentences.
The student chooses either
faster or slower and supports
the answer with references to
angular and linear velocity.
Student's response is written
in complete sentences.
The student chooses either
faster or slower and supports
the choice with references to
angular and linear velocity.
However, the student's
response is not written in
complete sentences.
The student’s response is written
in complete sentences but does
not directly reference angular and
linear velocity.
The student’s response does
not include a discussion of
angular and linear velocities
and is not written in complete
sentences.
The student correctly
calculates the revolutions per
minute for the 20-inch bike
and shows appropriate work
to support the answer.
The student incorrectly
calculates the revolutions per
minute. However, student shows
sufficient work so that 1-2 minor
errors can be found.
The student correctly calculates
the revolutions per minute.
However, the answer is not
supported by sufficient work.
The student incorrectly
calculates the revolutions per
minute and shows insufficient
work to support the answer.
Score:
Comments:
5. 20-inch bike
linear speed miles
per hour
Score:
Comments:
6. Revisit and revise
answer to Problem
1
Score:
Comments:
7. Faster or slower
for a 20-inch bike
Score:
Comments:
8. 20-inch bike
revolutions per
minute calculation
© K12 Inc.
Score:
Comments:
© K12 Inc.

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