Moment of Inertia Theorems

Moment of Inertia Definition

Moment of Inertia is the tendency of a body in rotational motion which opposes the change in its rotational motion due to external forces. The Moment of Inertia behaves as angular mass and is called rotational inertia. Moment of Inertia is analogous to the mechanical Inertia of the body....

What is Inertia?

Inertia is the property of a matter by virtue of which it tends to resist the change in the state of its motion. This means a body in rest tries to remain at rest and resist any force trying to bring it into motion, and a body in motion tries to continue in motion and resist any force trying to bring it to change the magnitude of its motion. In terms of quantity, it is equal to the maximum force trying to change its state of motion....

Moment of Inertia Formula

The Moment of Inertia is a scalar quantity. Mathematically, the product of the square of the mass of a particle and the distance from the axis of rotation is called the moment of inertia of the particle about the axis of rotation....

Moment of Inertia of a System of Particles

Moment of Inertia of a system of particles is given by the formula,...

Factors Affecting Moment of Inertia

Moment of Inertia of any object depends on the following values:...

How to Calculate Moment Of Inertia?

Several ways are used to calculate the moment of inertia of any rotating object....

Moment Of Inertia Formula for Different Shapes

This table discusses expressions for the moment of inertia for some symmetric objects along with their rotation axis:...

Radius of Gyration

The Radius of Gyration of a body is defined as the perpendicular distance from the axis of rotation to the point of mass whose mass is equal to the mass of the whole body and the Moment of Inertia is equal to the actual moment of inertia of the object as it has been assumed that total mass of the body is concentrated there. It is an imaginary distance. The Radius of Gyration is denoted by K....

Moment of Inertia Theorems

There are two types of theorems that are very important with respect to the Moment of Inertia:...

Perpendicular Axis Theorem

Perpendicular Axis Theorem states that the sum of the moment of inertia of a body about two mutually perpendicular axes situated in the plane of a body is equal to the moment of inertia of the body about the third axis which is perpendicular to the two axes and passes through their point of intersection....

Parallel Axis Theorem

According to Parallel Axis theorem, the moment of inertia of a body about a given axis is the sum of the moment of inertia about an axis passing through the center of mass of that body and the product of the square of the mass of the body and the perpendicular distance between the two axes....

Moments of Inertia for Different Objects

Moment of Inertia of different objects is discussed below in this article...

Difference Between Moment of Inertia and Inertia

The difference between inertia and moment of inertia is tabulated below:...

Kinetic Energy of Rotating Body

Let us assume a body of Mass ‘m’ rotating with velocity v at a distance ‘r’ from the axis of rotation. Its angular velocity is then given by ω = v/r then v = rω. Now we know that the Kinetic Energy of a body is given by...

Application of Moment of Inertia

Moment of Inertia has various applications some of which are discussed below:...

Solved Examples on Moments of Inertia

Example 1: A body of mass 500 g is rotating about an axis. the distance of the center of mass of the body from the axis of rotation is 1.2 m. find the moment of inertia of the body about the axis of rotation....

FAQs on Moments of Inertia

How to calculate the Moment of Inertia?...