Question

What is the principal moment of inertia?

Answer 1

In order to solve this question, we are going to first define the moment of inertia. Then, it is explained mathematically also. Then, the principal moment of inertia is defined along with an explanation to the calculation of the principal moment of inertia of the body which is considered.

Complete step-by-step solution:
A quantity that expresses the body’s tendency to resist the angular acceleration is called the moment of inertia. It is equal to the sum of the products of mass of each particle in the body with the square of its distance which is from the axis of rotation. The principal moment of inertia is one of the three moments of inertia , that is about its principal axes of inertia at a given point.
If we consider a figure for moments of inertia, which intersect at a point, the different lines that denote each moment of inertia are not equal to each other. If there is one line, which has the moment of inertia greatest, then, it is the least with respect to the line which is perpendicular to the first line. Relative to this point, the principal axes of inertia consist of a group of $3$ orthogonal lines. It consists of the first $2$ lines and a third line which is perpendicular to the principal line. If the point is the same as the figure’s central point, then the considered axes can be referred to as the principal axes of inertia. The moments of inertia which exist about these principal axes are called the principal moments of inertia.

Note: It is important to note that the principal moment of inertia is the most significant of all the moments of inertia. The moment of inertia is given by the equation$I = \dfrac{L}{\omega }$. Any axis that has symmetry with respect to its plane is the principal axis and inertia with respect to it is principal moment of inertia.