How to Calculate Rotational Kinematics for a Moving Bicycle?

AI Thread Summary
To calculate the rotational kinematics for a bicycle moving at 15.6 m/s with a wheel radius of 0.32 m, first determine the circumference of the wheel using C = 2πr. For part A, find the total distance for 19 rotations and divide by the bicycle's speed to get the time taken. For part B, convert 2.33 minutes to seconds to find the distance traveled, then calculate how many wheel rotations are needed to cover that distance. Each rotation corresponds to an angle of 2π radians. Understanding these calculations is essential for solving the problem accurately.
ScienceGirl90
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Homework Statement


Given a bicycle that is moving at a constant speed of 15.6 m/s with a wheel radius of .32 m...
A. How long will it take the wheel to rotate 19 times?
B. What angle in radians will the wheel rotate in 2.33 minutes?


Homework Equations


theta=angular velocity*time
s=radius*theta


The Attempt at a Solution


I need help understanding how to use what is given to plug it into the equations or if these equations are relevant to the problem. Thank you!
 
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A. Just think of the circumference of the wheel.
C=2pi r
What is the length of 19 circumferences?
How long will it take the bicycle to travel that distance if it is going at 15.6m/s?

B. How far does the bike travel in 2.33 mins? [You know its speed, convert time to seconds?]
You know the circumference of the wheel, so how many times must it spin to cover this distance?
Each time it spins it turns through 360 degrees, or 2pi radians.
 
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