Pulling a String Adds Energy to a Wheel

Learning Goal:

To apply the work-energy theorem to solve a planar kinetic problem.

(Figure 1)
A bicycle wheel, with moment of inertia I and radius r, is mounted on a fixed, frictionless axle, with a light string wound around its rim. The wheel is rotating counterclockwise with angular velocity ω1, 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.

 

 

Part A

Suppose that after a certain time, tL, the string has been pulled through a distance L. What is ω2, the final rotational speed of the wheel?

Express your answer in terms of L, F, I, and ω1.

ω2 =	(ω1)2+2FLI−−−−−−−−−−−−√

 

Part B

What is P, the instantaneous power delivered to the wheel via the force F at time t=0?

Express your answer in terms of some or all of the variables F, r, and ω1.

P =

Fω1r