What is Moment of inertia ?

Moment of inertia also referred to as rotational inertia, can be defined as the resistance provided by a body to its speed of rotation around an axis by the application of turning force often referred to as torque (Figure 1).

Or we can say it as, that moment of inertia is that quantity, which is expressed by the body resisting angular acceleration.

Angular acceleration can be mathematically defined as the sum of the product of the mass of every particle with its square of a distance from the axis of rotation.

When you will take science homework help our tutors talk about the total moment of inertia, it will be calculated as the sum of masses at a distance from the axis of rotation.

This topic is been studied in physics particularly. The SI unit of moment of inertia is kg m2.

Moment of inertia changes when there are different sizes, and shapes of the bodies are available.

Moment of inertia plays the same role as mass plays in linear motion, and it remains constant for a particular rigid frame, and the moment of inertia remains specific for the axis of rotation.

Figure 1: Figure showing moment of inertia around an axis.

It is a scalar quantity and has a formula that is expressed as I = m × r2
where,

m = Sum of the product of the mass.

r = Distance from the axis of the rotation.

and, Integral form: I = ∫dI = ∫0M r2 dm

⇒ The dimensional formula of the moment of inertia is given by, M1 L2 T0.

There are three factors on which moment of inertia depends; first is the density of the material, second is the shape and size of the considered body, and last is the axis of rotation.

For point-like mass, the formula of the moment of inertia is given by the distance of the point from the axis and is the mass.

For an extended rigid body, the formula of the moment of inertia is given by, the sum of all the small pieces of mass multiplied by the square of their distances from the axis in rotation.

A long body having a regular shape and having uniform density, will be given by the formula for the moment of inertia as, summation sometimes produces a simple expression that depends on the dimensions, shape and total mass of the object.

Thus, the formula of the moment of inertia for different objects can be seen in Figure 2.

Figure 2: Moment of inertia for different object

There are so many applications of the moment of inertia like

• While riding any vehicle, if the vehicle moves in a forward direction unexpectedly, a backward jerk can be felt by the person sitting over it or in it.

• To calculate stress, bending, and deflection in beams, we can use the moment of inertia of the area.

• Mass moment of inertia provides a way to measure an object’s resistance to change in the rotation direction.

• A wheel having more mass will lie near the axle, will speed up as it is easier for that wheel in comparison to the other wheel having equal mass, which is spread over a larger diameter.