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October 31, 2014

October 31, 2014

Posted by **igore** on Wednesday, February 2, 2011 at 4:00pm.

You are sitting on a stool that is free to rotate without friction, and you are holding a 2.0 kg weight in each hand (ignore friction and all forces external to you + weights system). Also ignore your own moment of inertia (pretend your moment of inertia is zero and that the moment of inertia of the you + weights system is determined entirely by the weights). You and your weights are rotating with an angular velocity of 3 radians per second, and you are holding the weights with arms outstretched so that each is 80.0 cm from the axis of rotation ( that is the distance from the axis to the center of mass of each weight). Then you pull your arms in so that weights are 20.0 cm from the axis of rotation.

a) What happens and why?

b) What is your angular velocity after you pull your arms in?

c) Keeping in mind what is and is not conserved as you pull in your arms, what are the initial and final kinetic energies of the rotating system?

d) Let the initial angular momentum of the system be L, the mass of one of the weights be M, and the distance from the axis of rotation to the blocks be R. (Note that if the angular momentum of the system is L, then the angular momentum of one of the blocks is L/2)

Then show that the force required to pull one of the blocks in at constant speed is equal to:

F=L^2/(4MR^3)

e) Now show that the magnitude of the work required to pull the blocks in from a distance of 80.0 cm to a distance of 20.0 cm really is equal to the difference in kinetic energy that you calculated in part c. That is, even if you couldn't derive it, use the formula for force given above and calculate the work done as you pull in the weights. Do not use conservation of energy to assert that the work is equal to the change in kinetic energy. Calculate the work done (using force as a function of distance) to show that it really is equal to the change in kinetic energy. There is an integral involved.

Thank you very much for any help for the above questions. Due tomorrow. Hopefully, my answers comes out like yours.

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