# Rotational Inertia Formula

## Rotational Inertia Formula

Inertia is the property of an object to resist forces that tend to move it or to change the magnitude or direction of its velocity while it is in motion. The Rotational Inertia Formula defines the same thing as rotating objects. This is a scalar value directly proportional to the mass and radius of the rotating object. In rotational mechanics, Rotational Inertia Formula functions similarly to mass in linear mechanics. It also depends on how that mass is distributed along the axis of rotation. It is used to calculate angular momentum and describe how rotational motion changes when the mass distribution changes.

Moment of inertia, also known as the angular mass or Rotational Inertia Formula, can be associated with an axis of rotation. It is expressed as a quantity that determines the amount of torque required to achieve a desired angular acceleration or the property of a body to resist angular acceleration. The moment of inertia formula is the sum of the mass products of each particle multiplied by the square of the distance from the axis of rotation. Students may wonder what is the moment of inertia.

The moment of inertia of an object is a specific measure of a rigid body that rotates about a fixed axis and axes can be internal or external and can be fixed or unfixed. However, the moment of inertia (I) is always written relative to this axis. The moment of inertia depends on the mass distribution around the axis of rotation. The MOI depends on the selected axis position. This means that the same object can have different moment of inertia values ​​depending on the position and orientation of the axis of rotation.

Angular mass or Rotational Inertia Formula is another name for the moment of inertia and the SI unit for the moment of inertia is kg m2.

• Example of the moment of inertia

Imagine one is sitting on a bus. One finds a place to sit. The bus starts moving. After a few minutes, one arrives at the bus stop and the bus stops. They may have experienced something at this point. When the bus stopped, their lower body did not move and their upper body moved forward. This happens due to inertia. The lower body is in contact with the bus, but the upper body is not in direct contact with the bus. When the bus stops, the lower body stays with the bus, but the upper body keeps moving forward. That is, it resists changes in state.

Similarly, when one gets on a moving train, one feels a force pushing them backwards. That is because they were resting before getting on the train. The moment they get on a moving train, their lower body touches the train, but their upper body is stationary. In other words, it resists changing its state.

### Rotational Inertia Formula

The Rotational Inertia Formula of a rotating body is equal to its mass times the radius of its orbit squared. It is represented by the symbol I. Its unit of measure is kgm2 and its dimension is given by [M1L2T0].

i = mr2

Where,

• I is the rotational inertia in Rotational Inertia Formula
• m will be the mass of the rotor
• r will be the radius of the circular path

### Sample Question

Question 1. Compute the Rotational Inertia Formula of an object with a mass of 20 kg and a radius of 4 m.

solution:

meters = 20

r = 4

Using the formula we have,

i = mr2

= 20 x 4 x 4

= 320kgm2

Question 2. Calculate the  Rotational Inertia Formula of a body with a mass of 25 kg and a radius of 6 m.

solution:

meters = 25

r = 6

Using the formula we have,

i = mr2

= 25 × 6 × 6

= 900kgm2

For more examples of the Rotational Inertia Formula, students can visit the Extramarks website.