What is moment of inertia of a rigid body

1.	What is moment of inertia of a rigid body
Answer» $\mathcal{MOMENT\:\:OF\:\:INERTIA}$ $\implies$ Moment of inertia of a body about a given axis is rhe sum of the products of masses of all the particles of the body and squares of their respective perpendicular distances from the axis of rotation. $\sf{I=\sum_{i=1}^{i=n}m_ir_i^2}$ The value of I DEPENDS upon: position of axis of rotation orientation of the axis of rotation shape of the body size of the body distribution of the MASS of the body about the axis of rotation. When the body does not consist of discrete particles, and has a continuous UNIFORM distribution of mass, the summation in above equation can be replaced by integration, $\sf{I=\int\:r^2\:dm}$ where dm is the mass of a small element of the body at a perpendicular distance r from the axis of raotation. If $\rho$ is the density of the body, then the mass of the small element of volume dV is $\sf{dm=\rho\:dV}$ $\sf{\therefore\:From\:above\:eqn.\:I=\int\rho\:r^2\:dV}$ Units of Moment of Inertia: As I = mass(distance)² ∴ Units of moment of inertia are KG m² or g cm². Dimensions of moment of inertia are $\sf{\left[M^1L^2T^0\right]}$

Answer»

$\mathcal{MOMENT\:\:OF\:\:INERTIA}$

$\implies$ Moment of inertia of a body about a given axis is rhe sum of the products of masses of all the particles of the body and squares of their respective perpendicular distances from the axis of rotation.

$\sf{I=\sum_{i=1}^{i=n}m_ir_i^2}$

The value of I DEPENDS upon:

position of axis of rotation
orientation of the axis of rotation shape of the body
size of the body
distribution of the MASS of the body about the axis of rotation.

When the body does not consist of discrete particles, and has a continuous UNIFORM distribution of mass, the summation in above equation can be replaced by integration,

$\sf{I=\int\:r^2\:dm}$