Question

Find the moment of inertia of a right circular cylinder about the cylindrical axis. Mass=M P is constant and v=pi(r)^2

Answer 1

I assume that the question says that the density is constant and that this is a solid cylinder of radius a and length l

The moment of inertia is defined as:

The infinitesimal mass can be written as:

Thus:

The limits of integration are:

On doing the integration we get:

since the term in the bracket is the total volume of the cylinder, if it is multiplied by the density, we get the total mass.