Question

If the height of a disk were somehow doubled while the radius is halved, and the mass stayed the same, how would the moment of inertia change?

Answer 1

Moment of inertia is depend on the radius and the mass of the disk .

It is no relate with the height of the disk

Now the moment of inertia of the disk having mass M and radius r is

Now the radius of the disk will become half i.e

R' = R/2

And mass has been unchange

Then the moment of inertia will become I'

This is the new moment of inertia of the disk

i.e

I' = I/8

i.e the moment of inertia will become 1/8 times the initial moment of inertia .