The mass moment of inertia of the differential mass dm about 0-0 axis (perpendicular to the plane of rotation of centre of mass) is
dI = r2 dm
I = ʃ r2 dm
where I is the mass moment of inertia of the body of mass m. It is obvious that we take into account of mass moment of inertia for rotational motion of a body.
If the mass density pis kept constant, we can write dm = p dV. where dV =element
(8.1) => I = ʃ r2 p dV =P ʃ r2 dV