Weight and Wheel
Consider a bicycle wheel that initially is not rotating. A block of mass is attached to the wheel and is allowed to fall a distance . Assume that the wheel has a moment of inertia about its rotation axis.
Part A
Consider the case that the string tied to the block is attached to the outside of the wheel, at a radius

. Find , the angular speed of the wheel after the block has fallen a distance , for this case.
Hint A.1 Hint not displayed
Part A.2 Part not displayed
Part A.3 Part not displayed
Part A.4 Part not displayed
Express in terms of , , , , and .
ANSWER:
 = (2*m*g*h/(m*r_A^2+I))^(1/2)
Part B
Now consider the case that the string tied to the block is wrapped around a smaller inside axle of the wheel of radius . Find , the angular speed of the wheel after the block has fallen a distance , for this case.
Hint B.1 Hint not displayed
Express in terms of , , , , and .
ANSWER:
 = (2*m*g*h/(m*r_B^2+I))^(1/2)
Part C
Which of the following describes the relationship between and ?
Hint C.1 Hint not displayed
ANSWER:
This is related to why gears are found on the inside rather than the outside of a wheel.
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