Rotational Inertia Formula

Introduction

Rotational inertia, or moment of inertia, is a fundamental concept in rotational dynamics, just as mass is in linear motion. In general, the rotational inertia will describe the resistance of an object to changes in its rotational state. It is a crucial ingredient in explaining the way bodies rotate and a central element in many applications, ranging from engineering to physics.

Formula for Rotational Inertia

The formula for rotational inertia I depends upon the distribution of the mass of the object relative to the axis of rotation. The general formula is:

  I=mr2

Where,

• I = rotational inertia

• m = mass of the object

• r = radius of the circular path

Solved Problem

Problem 1: Find the rotational inertia of an object that has a mass of 20kg and that is rotating with a radius of 8m.

Solution:

Given

Mass of object, m = 20kg

Radius of rotation, r= 8m

The Formula of rotational inertia is

I=mr2

I=20 × 82

I= 1280 kgm2

Problem 2: Calculate the rotational inertia of a point mass of 50 kg located 3 meters from the axis of rotation.

Solution:

Given:

Mass of object, m = 50kg

The radius of rotation, r = 3m

For a point mass, the formula for rotational inertia I is:

  I=mr2

  I=50kg32

  I=450kgm2