question followed by an experiment of dropping a non-rotating rod on a circular

Question

question followed by an experiment of dropping a non-rotating rod on a circular disc (no external torque):

1. what if the rod were already rotating at the same angular veolocity as the disc before you dropped it onto it-- would the disc's angular velocity change after dropping? why or why not?

question followed by an experiment of using a small mass to rotate the circular disc (external torque):

2 if you were a bug (instead of the falling mass) hanging from the string wrapped around the same pulley you used in the lab, and you wanted to descend to the lab table as softly as possible, so as not to squash yourself. you have your choice of discs--the usual one or the one with half the mass but twice the radius-- which one would you prefer? remember you are only swapping the disc part of the set up.

Explanation / Answer

if the rod is not rotating then then after dropping the moment of inertia of the whole setup increses and as Angular momentum Iw is constant

and I of system increses thus the velocity has to decrese

but if the rod was also rotating at the same angular velocity and then its dropped then there will be no change in the velocity as the intial and final angualr momentums will be same thus there is no alteration in the I and w of the system

now for the other question

the disc with the momnet of inertia of the 2 dics will be

1) .5 x m x r^2

2) .5 x .5m x 4 r^2

thus we see the moment of inertia of the bigger radius disk is twise the smaller one so the angular velocity of the smaller disk is double that of the bigger disk

thus the bigger disk will have more smmoth operation thus the choice will be for the bigger disk

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