Question

Mass moment of inertia of cylinder perpendicular to length

Answer 1

the moment of inertia of a solidcylinder about its own axis is the same as its moment of inertia about an axis passing through its centre of gravityand perpendicular to its length.the relation between its length L and radius R is---.

Answer 2

We will consider the cylinder having mass M, radius R, length L and the z-axis which passes through the central axis.

Here,

Density ρ = M / V

Next, we will consider the moment of inertia of the infinitesimally thin disks with thickness dz.

First, we assume that dm is the mass of each disk, We get;

dm = ρ X Volume of disk

dm = M / V X (πr2.dz)

We take V = area of circular face X length which is = πr2L. Now we obtain;

dm = M / πr2L X (πr2.dz)

dm = M / L X dz

The moment of inertia about the central axis is given as;

dlz = ½ dmR2