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Moment of Inertia

Moment of Inertia is a quantity which describes body’s tendency to resist angular acceleration. In other words it is the measure of the amount of moment provided to a body to conquer its own inertia. It describes about the object offering resistance to accelerate or slow down its own motion.

It is the sum of the products of the mass of every component in the body with the square of the distance from the point of rotation.  

Moment of inertia formula is given by

I = MR²

Where,

R is the Distance between the axis and rotation in m

M is the Mass of the object in Kg

I =  Moment of Inertia in Kgm²

It’s based on the shape and mass distribution of the body and also on the orientation of the rotational axis

moment of Inertia

Example 1

Determine the Moment of inertia of the ball having mass of 10 Kg and radius of 5 cm.

Solution:

Given parameters are,

Mass of the ball = 10 Kg,

Radius = 5 cm

= 0.05 m,

Moment of Inertia is given as

I = MR²

 = 10 × (0.05 )²

 = 0.025 Kgm²

Example 2

A sphere is moving around and its moment of inertia is 20 Kgm² and radius 1 m, determine its mass.

Solution:

Given:

Moment of inertia, I = 20 Kgm²,

Radius of sphere, R = 1 m,

Moment of Inertia formula is given by,

I = MR²

M = I / R²

       = 20 / 1

       = 20 Kg