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Question

A solid cylinder of mass, m, and radius, r, is rotating at an angular velocity, ω when a non-rotating cylinder of double the mass and equal radius drops onto the cylinder.
By what factor does this change the rotational kinetic energy with regard to its initial rotational kinetic energy Krot?

A
Krot=3Krot
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B
Krot=13Krot
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C
Krot=9Krot
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D
Krot=19Krot
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E
Krot=Krot
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Solution

The correct option is C Krot=13Krot
Moment of inertia of the solid cylinder I=12mr2
Thus initial kinetic energy of the system Krot=12Iw2=14mr2w2

Final moment of inertia of the system I=12mr2+12(2m)r2=32mr2

Let the final angular velocity of the system be w.
Using conservation of angular momentum : Iw=Iw
12mr2w= 32mr2w w=w3

Thus final kinetic energy of the system Krot=12I(w)2=112mr2w2
Krot=Krot3

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