Question

From a disc if a cavity is removed what is the net moment of inertia

Answer 1

Hey.

Here is the answer.

Because the moment of inertia for a point mass is:

I=mr^2

When calculating the moment of inertia for continuous bodies we use calculus to build them up from infinitesimal mass elements, so effectively to calculate the moment of inertia of the disk (without hole) we're doing:

Idisk=∑disk mr^2

for the collection of infinitesimal masses mimi that make up the disk. When you create a hole you simply subtract off all the point masses in the hole to remove them from the sum:

Inet=∑disk m r^2−∑ hole m r^2

where the second sum is over all the infinitesimal masses in the bit you're removing to make the hole. So you end up with:

Inet = Idisk−Ihole

So, Inet will give required moment of inertia .

Thanks.