Question

what is moment of inertia of a rigid body​

Answer 1

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

$\implies$ 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:

1. position of axis of rotation  
2. orientation of the axis of rotation  shape of the body
3. size of the body  
4. 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 2

Answer:-

• The moment of inertia, otherwise known as the mass moment of inertia, angular mass or rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for a desired acceleration.
• Moment of Inertia. The moment of inertia is sometimes called and referred to as "angular mass." It is the "amount of resistance" to rotational motion. ... The moment of inertia is commonly used to calculate torque when multiplied by the angular acceleration.
• Moment of inertia about a given axis of rotation resists a change in its rotational motion; it can be regarded as a measure of rotational inertia of the body.
• The formula for moment of inertia is the “sum of the product of mass” of each particle with the “square of its distance from the axis of the rotation”. The formula of Moment of Inertia is expressed as I = Σ MiRi²

i hope it helps you.