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A solid cylinder of mass, m, and radius, r is rotating at an angular velocity, $\omega$ 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 $K_{rot}$?

A

${ K }_{ rot }^{ \prime }=3{ K }_{ rot }$

B

${ K }_{ rot }^{ \prime }=\frac{1}{3}{ K }_{ rot }$

C

${ K }_{ rot }^{ \prime }=9{ K }_{ rot }$

D

${ K }_{ rot }^{ \prime }=\frac{1}{9}{ K }_{ rot }$

E

${ K }_{ rot }^{ \prime }={ K }_{ rot }$

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