Find the moment of inertia of this disk

[234jazzy2]

Homework Statement

A crucial 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
Express your answer in terms of the variables M, R0, R1, and h.

How do i convert mass of the cutout in terms of overall mass?

Homework Equations

I = (1/2)mr^2

The Attempt at a Solution

I = (1/2)M(R0)^2 - I cutout
I cutout = (1/2)m(R1)^2 + mh^2

Thanks

 

[collinsmark]

Hello @234jazzy2 ,

Welcome to Physics Forums!

Homework Statement

A crucial 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
Express your answer in terms of the variables M, R0, R1, and h.

How do i convert mass of the cutout in terms of overall mass?

Are you inquiring about how to find the mass of the cutout?

Before the hole was drilled, the overall disk had a particular area that you can calculate. And the overall disk has a known mass, M. With those you can calculate the disk's mass per unit area. That's sort of like the density of the disk.

Then calculate the area of the drilled out hole section. Since you know the area of the cutout and the disk's mass per unit area ("density" like characteristic) you should be able to determine the mass of the cutout.

Homework Equations

I = (1/2)mr^2

The Attempt at a Solution

I = (1/2)M(R0)^2 - I cutout
I cutout = (1/2)m(R1)^2 + mh^2

It looks like you are on the right track so far.

 

[234jazzy2]

Hello @234jazzy2 ,

Welcome to Physics Forums! Are you inquiring about how to find the mass of the cutout?

Before the hole was drilled, the overall disk had a particular area that you can calculate. And the overall disk has a known mass, M. With those you can calculate the disk's mass per unit area. That's sort of like the density of the disk.

Then calculate the area of the drilled out hole section. Since you know the area of the cutout and the disk's mass per unit area ("density" like characteristic) you should be able to determine the mass of the cutout.
It looks like you are on the right track so far.

Thanks! Didn't know you could think of it in terms of density.