Moments of Inertia for Different Objects
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