Question

Derivation for mass momentum of inertia of a circle

Answer 1

In physics, the rotational equivalent of mass is something called the moment of inertia. The definition of the moment of inertia of a volume element

dV

which has a mass

dm

is given by

dI = r_{\perp}^{2} dm

where

r_{\perp}

is the perpendicular distance from the axis of rotation to the volume element. To find the total moment of inertia of an object, we need to sum the moment of inertia of all the volume elements in the object over all values of distance from the axis of rotation. Normally we consider the moment of inertia about the vertical (z-axis), and we tend to denote this by

I_{zz}

. We can write

I_{zz} = \int _{r_{1}} ^{r_{2}} r_{\perp}^{2} dm

The moment of inertia about the other two cardinal axes are denoted by

I_{xx}

and

I_{yy}

, but we can consider the moment of inertia about any convenient axis.