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Moment of Inertia Calculator
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The moment of inertia of an object about an axis is defined as the sum of the products of the masses of different particles and square of their perpendicular distances from the axis of rotation. It is given by I = MD2
where I = Moment of Inertia, in kg-m2
D = Distance between the axis and rotation in m
M = Mass of the object in Kg.
It is the resistance that is shown by the object to change its rotation. I and J are used as symbols for denoting moment of inertia.

Moment of inertia of a body depends on

1)The mass of the body.

2)The position of the axis of rotation and

3)The distribution of the mass of the body about the axis.

Moment of Inertia Calculator calculates the Inertia, if mass of the object and distance between axis and rotation are given using the formula. It also calculates mass of the object or distance between axis and rotation, if we know any of the two parameters either mass, distance or inertia.
I = M × D2
where:
I = Moment of Inertia, in kg-m2
D = Distance between the axis and rotation in m
M= Mass of the object in Kg.

Steps for Calculating Moment of Inertia

Step 1 :

Moment of inertia Formula:

Inertia(I) = MD2

Mass of the object(M) = $\frac{I}{D^{2}}$

Distance between the axis and rotation(D) = $\sqrt{\frac{I}{M}}$
where I = Moment of Inertia, in kg-m2
D = Distance between the axis and rotation in m
M = Mass of the object in Kg.

Step 2 :

State the equation you plan to use and plug in the values.

Moment of Inertia Problems

1. A sphere is moving round, it has a mass of 3 kg and radius of 2 m. Calculate its moment of inertia?

Step 1 :

Given that:

Mass of the sphere(M) = 3 kg

Distance(D) = 2m

Moment of Inertia(I) = ?

Step 2 :

Substitute the given values in the formula:

Moment of Inertia(I) = MD

Moment of Inertia(I) = 3kg $\times$ (2m)2

Moment of Inertia(I) = 12 kg-m2

Moment of Inertia(I) = 12 kg-m2

2. A ball is moving round, if the moment of inertia and radius is 14 kg-m2 and 4m, then calculate its mass?

Step 1 :

Given that:

Mass of the sphere(M) = ?

Distance(D) = 4m

Moment of Inertia(I) = 14 kg-m2

Step 2 :

Substitute the given values in the formula:

Mass of the object(M) = $\frac{I}{D^{2}}$

Mass of the object(M) = $\frac{14 kg-m^{2}}{(4m)^{2}}$

Mass of the object(M) = 0.875 kg