Question

What is the physical importance of the moment of inertia?

Answer 1

Hint: In order to answer the above question, we will learn about the topic of moment of inertia. We will understand what we basically mean by moment of inertia and then derive its physical importance using all that information.

Complete step by step solution:
First of all, we will understand the term moment of inertia.
Newton's first law of motion, also known as the law of inertia, states that a body cannot change its state of rest or uniform motion along a straight line by itself. Inertia is the term for this property of inertness. It is a characteristic of matter. A body resists any alteration in its state of rest or uniform motion in a straight line due to inertia.
The sum of the products of the mass of each and every particle of the body and the square of its distance from the given axis is the moment of inertia of a rigid body around a given axis.
$I=m{{r}^{2}}$
Where $I$ is the moment of inertia, $m$ is the mass and $r$ is the distance from the axis.
The mass of a body in translational motion is a measure of its inertia. The greater the mass, the greater the inertia, and the greater the force needed to achieve a given linear acceleration. The moment of inertia of a body is a measure of its inertia in rotational motion. The torque needed to achieve a given angular acceleration in it increases as the moment of inertia increases.
Thus, the moment of inertia in the rotational motion is analogous to the mass in translational motion because it plays the same role in rotational motion as the mass plays in translational motion. And hence, the moment of inertia is of great importance physically.

Note:
It is very important to note that the moment of inertia is not similar to the friction experienced by the body. Both the friction and the moment of inertia plays a different role and are different from each other. The moment of inertia is just the replacement of mass in the calculations of physical quantities in rotational motion as compared to the translational motion.