Unit of Moment Of Inertia

Moment of inertia from a Physics point of view is basically a quantitative measure of the rotational inertia or the angular mass of a body. In simple terms, it is the opposition that the body exhibits to the change in rotation about an axis which may further be internal or external.

The moment of inertia (I) is mostly specified based on the distribution of mass in the body with respect to the axis of rotation.

Moment of Inertia Units

Following are the two types of moment of inertia with their formula:

  1. Area moment of inertia: mm4 or in4
  2. Mass moment of inertia: kg.m2 or ft.lb.s2

Dimensional Formula: M1L2T0

What is the SI Unit of Moment of Inertia?

The SI unit of moment of inertia is: kg.m2

Interested to learn about units of other Physics quantities, below is the link:

Moment Of Inertia Of Rigid Body

Following are the moment of inertia for rigid objects:

Rigid object Moment of inertia
Solid cylinder \(I=\frac{1}{2}MR^{2}\)
Solid cylinder central diameter \(I=\frac{1}{4}MR^{2}+\frac{1}{12}ML^{2}\)
Rod about centre \(I=\frac{1}{12}ML^{2}\)
Hoop about the symmetry axis \(I=MR\)
Hoop about diameter \(I=\frac{1}{2}MR^{2}\)
Thin spherical shell \(I=\frac{2}{3}MR^{2}\)
Rod about end \(I=\frac{1}{3}ML^{2}\)

Conversion Between Moment of Inertia Units

Following is the table with the moment of inertia unit conversion:

Unit kg. m2 g.cm2 lbmft2 lbmin2
kg. m2 1 1×107 2.37×10 3.42×103
g.cm2 1×10-7 1 2.37×10-6 3.42×10-4
lbmft2 4.21×10-2 4.21×105 1 1.44×102
lbmin2 2.93×10-4 2.93×103 6.94×10-3 1

Example of Moment of Inertia 

Consider a wheel and a uniform disc, both having the same mass rotating about the same axis. If you may have observed, it is difficult to start or stop the wheel than it is to start or stop the uniform disc.

Why is this so, in spite of both the objects having the same mass?

This is because the force required to stop a rotating object is directly proportional to the product of the mass and the square of the distance from the axis of rotation to the particles that make up the body.

Mathematically, it is represented as F = mr2

In this case, the mr2 of the wheel > mr2 of the disc.

This explains why it is difficult to rotate a wheel compared to a uniform disc.

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