posted by Gabe on .
A bicycle wheel is mounted on a fixed, frictionless axle. A massless string is wound around the wheel's rim, and a constant horizontal force, F, starts pulling the string from the top of the wheel starting at time t = 0 when the wheel is not rotating. Suppose that at some later time t the string has been pulled through a distance d. The wheel has moment of inertia I(subW) = kmr^2, where k is a dimensionless number less than 1, m is the wheel's mass, and r is its radius. Assume that the string does not slip on the wheel.
The force, F, pulling the string is constant; therefore the magnitude of the angular acceleration, alpha, of the wheel is constant for this configuration.
Find the magnitude of the angular velocity, omega, of the wheel when the string has been pulled a distance, d.
Express the angular velocity, omega, of the wheel in terms of the displacement, d, the magnitude of the applied force, F, and the moment of inertia of the wheel, I(subW).