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AP® Physics C: Mechanics

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Rotational Inertia: Disk with a Large Hole in It

APPHMC-PSRDC8

A disk of uniform density has an outer radius of $R_o$ and a large hole in the center with a radius of $R_i=1/3 \text{ }R_o$. It has a mass of $M$. The equation for the rotational inertia, $I$, of a solid disk around its center is $1/2 \text{ }MR^2$.

Determine the rotational inertia, $I$, of this disk with a large hole in it?

A

$I=\cfrac {1}{9}MR_o^2$

B

$I=\cfrac {4}{9}MR_i^2$

C

$I=\cfrac {4}{9}MR_o^2$

D

$I=\cfrac {1}{2}MR_o^2$

E

$I=\cfrac {5}{9}MR_o^2$