Posted by **Sleepless** on Saturday, April 12, 2008 at 4:13am.

A curcial part of a piece of machinery starts as a flat uniform cylindrical disk of radius R0 and mass M. It then has a circular hole of radius R1 drilled into it. The hole's center is a distance h from the center of the disk. Find the moment of inertia of this disk (with off-center hole) when rotated about its center, C.

Hint: Consider a solid disk and subtract the hole; use parallel-axis theorem.

- physics -
**drwls**, Saturday, April 12, 2008 at 7:35am
The moment of inertia of the disc before the hole is drilled is

I0 = (1/2) M R0^2.

From that, SUBTRACT the moment of inertia of what the hole would be, if it were solid and displaced h from the center.

Its mass would be m = M(R1/R2)^2

Using the parallel axis theorem, its moment of inertia would be

I' = (1/2)m R1^2 + m h^2.

Subtract I' from I0 for the answer. Don't forget to substitute M(R1/R0)^2 for m.

- physics -
**Thanks**, Saturday, April 12, 2008 at 5:08pm
much thanks!

## Answer This Question

## Related Questions

- Physics - A machine part is made from a uniform solid disk of radius R and mass ...
- Physic - A machine part is made from a uniform solid disk of radius R = 0.161 m ...
- Physics! - The figure shows a uniform disk with a circular hole cut out of it. ...
- Physics - A solid cylindrical disk has a radius of 0.18 m. It is mounted to an ...
- physics - A solid cylindrical disk has a radius of 0.17 m. It is mounted to an ...
- Physics - A flat uniform circular disk (radius = 2.10 m, mass = 1.00 102 kg) is ...
- physics - A solid cylindrical disk has a radius of 0.16 m. It is mounted to an ...
- Physics - A thin rectangular plate of uniform area density σ1 = 1.01 kg/m2 ...
- physics - A thin rectangular plate of uniform area density σ1 = 1.00 kg/m2 ...
- physics - A spherical shell of uniform charge density σ has a circular hole...

More Related Questions