Consider a CD rotating freely in a horizontal plane (i.e. the axis of rotation i

Question

Consider a CD rotating freely in a horizontal plane (i.e. the axis of rotation is vertical) about a fixed frictionless rod passing through the center of the CD. A drop of mud falls straight down and lands on the CD mid-way between the axis and the rim. Consider each of the conservation laws you know of: momentum, energy, and angular momentum. Can any of these be applied to the system comparing its state just before the mud landed to its state just after the mud landed? !!! For each one, explain why or why not. Help needed! Please explain in details for every law, why it's possible or not. Thanks!!

Explanation / Answer

say initially moment of inertia of the system=I

moment of intertia including mud=I'=I+mr^2

m=mass of drop of mud ;r=distaance from axis of rotation

conserving angular momentum

I=I''

also angular KE

.5I^2=.5I''^2

As drop of mud falls straight down,there is no motion along horizontal,also the rotating cd has not any translational movement ,therefore coservation of momentum is not useful.

Conserving angular momentum and angular KE is crucial in this case ,because above explanation shows that there is change in moment of inertia of the system thats .

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