Moments of Inertia for Different Objects

Difference Between Moment of Inertia and Inertia

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

Moment of Inertia of a Rectangular Plate

If the mass of the plate is M, length l, and width b, then the moment of inertia passes through the center of gravity and about an axis perpendicular to the plane of the plate.

I = M(l² + b² / 12)

Moment of Inertia of a Disc

If the disc has a mass M and radius r, then the moment of inertia about the disc’s geometric axis is

I = 1/2(Mr²)

Moment of Inertia of a Rod

If the mass of the rod is M and the length is l, then the moment of inertia about the axis perpendicular to the length of the rod and passing through its center of gravity

I = ML²/12

Moment of Inertia of a Circle

If the mass of the ring is M and the radius of the ring is r, then the moment of inertia about the axis passing through perpendicularly to the center of the ring is

I = Mr²

Moment of Inertia of a Sphere

If a Solid Sphere has a mass of M and a radius of r, then the moment of inertia about its diameter is

I = 2/5Mr²

Moment of Inertia of Solid Cylinder

The Moment of Inertia of a Solid Cylinder of Radius ‘R’ and mass M is given by

I = 1/2MR²

Moment of Inertia of Hollow Cylinder

A hollow cylinder has two radii namely internal radius and external radius. The Moment of Inertia of a Hollow Cylinder having mass M, external radius R₁, and internal radius R₂ is given as

I = 1/2M(R₁² + R₂²)

Moment of Inertia of Solid Sphere

The Moment of Inertia of a Solid Sphere of Mass ‘M’ and Radius ‘R’ is given as

I = 2/5MR²

Moment of Inertia of Hollow Sphere

The Moment of Inertia of a Hollow Sphere of Mass M and Radius ‘R’ is given as

I = 2/3MR²

Moment of Inertia of Ring

The Moment of Inertia of a Ring is given for two cases when the axis of rotation passes through center and when the axis of rotation passes through the diameter.

The Moment of Inertia of the Ring about the axis passing through the center is given by

I = MR²

The Moment of Inertia of the Ring about the axis passing through the diameter is given by

I = Mr²/2

Moment of Inertia of Square

The Moment of Inertia of the Square of side ‘a’ is given as

I = a⁴/12

The Moment of Inertia of a Square Plate of the Side of length ‘l’ and mass M is given as

I = 1/6ML²

Moment of Inertia of Triangle

The Moment of Inertia of a Triangle is given for 3 situations, first, when axis pass through the centre, second when axis pass through the base and third when axis is perpendicular to the base. Let’s see the formula for them one by one. For a triangle of base ‘b’ and height ‘h’, the formula for moment of inertia is given as follows

When axis pass though the Centroid

I = bh³/36

When axis pass through the Base

I = bh³/12

When axis is Perpendicular to the base

I = (hb/36)(b² – b₁b + b₁²)

Moment of Inertia

Moment of inertia is the property of a body in rotational motion. Moment of Inertia is the property of the rotational bodies which tends to oppose the change in rotational motion of the body. It is similar to the inertia of any body in translational motion. Mathematically, the Moment of Inertia is given as the sum of the product of the mass of each particle and the square of the distance from the rotational axis. It is measured in the unit of kgm².

Let’s learn about the Moment of Inertia in detail in the article below.

Table of Content

Moment of Inertia Definition
Moment of Inertia Formula
Factors Affecting Moment of Inertia
How to Calculate Moment Of Inertia?
Moment Of Inertia Formula for Different Shapes
Radius of Gyration
Moment of Inertia Theorems
Moments of Inertia for Different Objects