Problem:

A bicycle wheel is mounted on a fixed, frictionless axle, with a light string wound around its rim. The wheel has moment of inertia I=kmr2, where m is its mass, r is its radius, and k is a dimensionless number between zero and one. The wheel is rotating counterclockwise with angular velocity (SYMBOL1), when at time t=0 someone starts pulling the string with a force of magnitude F.

Assume that the string does not slip on the wheel.

A. Suppose that after a certain time tL, the string has been pulled through a distance L. What is the final rotational speed of the wheel?

Express (SYMBOL1) in terms of L, r, F, k, m and (SYMBOL2)

B. What is the instantaneous power delivered to the wheel via the force F at time T=0?

Express the power in terms of the variables given in the problem introduction.

(PLEASE SEE ATTACHMENT FOR PROPER SYMBOLS AND DIAGRAM)

Pulling a String Adds Energy to a Wheel

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Assume that the string does not slip on the wheel.

. What is the final rotational speed of the wheel?

.

?

Express the power in terms of the variables given in the problem

introduction.

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