Moment of InertiaConcepts

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What is Moment of Inertia• The moment of inertia of a system about some rotational point is the

measure of an object's resistance to a change in the object's angular acceleration due to the action of a torque

• The below quantity tell us how the mass of the rotating body is distributed about the axis of rotation is known as moment of inertia of the rotating body

• Moment of inertia of the rigid body can be obtained by imaging the body to be subdivided into large number of particles ,the mass of the each particle is then multiplexed by its squared distance from the axis and then summing over these products for all the particles in the body

• Si unit of moment of inertia is Kgm2

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Important points for Moment of Inertia

• The moment of inertia depends upon how an object's mass is distributed relative to it pivot point.

• A body does not have just one moment of inertia but potentially an infinite number of I's, one for every different pivot point.

• It is the rotational analog of mass for linear motion. It appears in the relationships for the dynamics of rotational motion

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Moment of Inertia Theorem’s

Perpendicular axis theorem

Iz=Ix+IY

This theorem states that,

the moment of inertia

of a plane laminar about

an axis perpendicular to its

plane is equal to the sum

of the moment of inertia of

the lamina about two axis

mutually perpendicular to

each other in its plane

and intersecting each other

at the point where

perpendicular axis passes

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Moment of Inertia Theorem’s

Parallel axis theorem

Ix=IY+Mr2

This theorem states that Moment

of inertia of body about an axis X parallel to another axis

Y is equal to the sum of Moment

of inertia about axis Y plus

the product of mass and square

of distance between the axis

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Example

Moment of Inertia of solid diskabout an central axis

2

21MRI

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Example

Moment of Inertia of solid sphere around central axis of Sphere

2

52MRI

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