Question

What is moment of inertia? Distinguish between area moment of inertia, polar moment of inertia and mass moment of inertia.

Answer 1

I think your question suggests that you are confused between rotational motion of a body and twisting of a body.

So to clear that up, rotational motion of a body is a stress free state of a body , it means that the force or in case of rotational motion the torque being applied is being completely used to rotate the body and there is no opposing torque to generate stress in the body . In such case mass moment of inertia is the physical quantity used as it is the resistance to rotational motion .

On the other hand twisting motion can be applied to a body when there are two torques acting on a body in opposite directions , which means as the body is in static equilibrium because the total torque on the body is zero, it would not come into motion and only deformation will occur in the body. In this casepolar moment of inertia is the physical quantity used as it is the resistance to the twisting deformation or torsional stresses developed in the body.

To simplify things consider this analogy it will give you a proper essence of the difference in the two quantities.

Mass is nothing but a resistance to motion similarly mass moment of Inertia is resistance to rotational motion.Area is a resistance to stress developed similarly polar moment of inertia is resistance to torsional stresses developed.

Answer 2

moment of inertia is law of first Newton motion is also called Law of Inertia of moment of inertia polar moment of inertia and mass moment of inertia I don't know that it is but it is what is inertia means it is law of law of motion of first law of motion Newton