A large plate is balanced at its center and two students of equal mass stand at

Question

A large plate is balanced at its center and two students of equal mass stand at its center. The plate is rotated on a frictionless pivot about an axis through its center and perpendicular to its face. The students then begin to walk out towards opposite edges.
(Select T-True, F-False, I-Increases, D-Decreases, S-Stays the same. ).  

A) The students do work in walking outward.
B) When the students reach the edge and stop, the plate will have the same angular speed as when they started.
C) The students produce a net torque on the plate.
D) The total angular momentum of the system ... as the students walk outward.
E) The rate of rotation ... as the students walk outward.

I need the correct answer in order to give full rating.

Explanation / Answer

A) See C) Since the net torque is zero, the total work W = tau phi, where phi is the rotational angle, is zero asw ell.

B) See E)

C) No. There is not net torque since the torques caused by the students are always equal and opposite, assuming that they walk always at the same rate, and that they finally reach the same distance from the center.

D) Since there is no net torque tau, the angular momentum S does not change: indeed, it is dS / dt = tau.

E) Nonetheless, since, roughly speaking, S = I omega, with them moment of inertia I = M R^2, and S = const., then omega must decrease. Indeed, the moment of inertia gets larger because the students move outward increasing R.

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