you are helping to design an apparatus that measure rainfall. It consists of two

Question

you are helping to design an apparatus that measure rainfall. It consists of two identical cups on either end of an arm that rotates around a frictionless pivot. RIght before the rain starts a motor starts the cups spinning. Assuming no other forces are exerted on the cups and spinning arm (i.e. you can ignore friction and the motor isn't pushing anymore), what will happen to the cups as they fill up with rain? (assuming the rain falls straight down)

A) the cups will slow down because the rain loses KE when they hit the cup.

B) the cups continue to rotate at a constant angular velocity because the total Mechanical Energy of the bucket plus rain system is conserved.

C) the cups slow down because angular momentum of the cups plus rain system about the pivot point is conserved.

D) the cups speed up because the PE of the rain is transformed into KE

E) the cups contintue to rotate at a constant angular velocity because the rain is falling straight down while the bucket moves in a horizontal plane.

F) None of the above are correct.

Explanation / Answer

C) the cups slow down because angular momentum of the cups plus rain system about the pivot point is conserved.

This is Because as the water in the Cups Increase then the Moment of Inertia Also Increases because I = mr^2 , So m increasese So I increases

And Angular Momentum = IW = Constant

As I increases then W will decrease to make angular momentum constant

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