A small hamster of mass \"m\" is running at constant speed on a hamster wheel of

Question

A small hamster of mass "m" is running at constant speed on a hamster wheel of mass "M" and radius "R". (In other words, his feet are moving with respect to the wheel, but he is stationary with respect to the table and it is the wheel which is spinning.) (Express your answers in terms of these given quantities. Assume that the wheel is a hoop and the hamster is a point particle at the rim.)

Suddenly freaked out by something, the hamster grabs ahold of the wheel with his claws. The hamster rides the wheel "up and around", coming to a stop with the hamster exactly at the top. (He hangs on, does not fall off.) What angular velocity "" must the wheel + hamster system have had the instant after the hamster grabbed ahold?

What was the original "" of the wheel, before the hamster grabbed ahold?

Explanation / Answer

Angular momentum is conserved.
So if the wheel has a mass m, it is moving at a tangential velocity of v,and the hampster has a mass M
then the velocity of the periphery of the wheel after the hamster grabs it will be V2= mv/(M+m)

It will have a kinetic energy of 1/2 (m+M) V2^2 = 1/2 (m+M) m^2 v^2 / ( M+m)^2
= 1/2 m^2 v^2 / ( M+m)

This energy must be sufficient to raise the hamster a height h
Mgh = 1/2 m^2 v^2 / ( M+m)

v^2 = 2 Mgh(M+m)/ m^2
v=sqrt( 2 Mgh(M+m)/ m^2)

And as the angular velocity = v/R = v/(h/2) = 2v/h

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