A disk of radius R has an initial mass M . Then a hole of radius 14 R is drilled

Question

A disk of radius R has an initial mass M. Then a hole of radius 14R is drilled, with its edge at the disk center(see the figure (Figure 1) ).

Part A

Find the new rotational inertia about the central axis. Hint: Find the rotational inertia of the missing piece, and subtract it from that of the whole disk. You

A disk of radius R has an initial mass M. Then a hole of radius 14R is drilled, with its edge at the disk center(see the figure (Figure 1) ).

Part A

Find the new rotational inertia about the central axis. Hint: Find the rotational inertia of the missing piece, and subtract it from that of the whole disk. You

Explanation / Answer

mass of missing piece = R/4*R/4 * M/R*R = M/16

moment of inertia of missing piece about central axis ofM disk.

= 1/2*M/16 * R/4*R/4 + M/16 * R/4*R/4 = 3/2* M/16* R*R/16

= 3MR2/512

new rotational inertia = 1/2*M*R*R -3MR2/512 = 253MR2/512

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