Assignment linear velocity application

User Generated

Nylffn1997

Mathematics

Unformatted Attachment Preview

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.
Purchase answer to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer


Anonymous
Super useful! Studypool never disappoints.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4