Moment of inertia is a measure of an object's resistance to changes in its angular acceleration due to an applied torque. It depends on how the object's mass is distributed relative to its pivot point. The moment of inertia of a rigid body can be calculated by imagining it divided into particles, multiplying each particle's mass by the square of its distance from the axis of rotation, and summing these values. Important theorems for calculating moment of inertia include the perpendicular axis theorem and parallel axis theorem. Examples are given for calculating the moment of inertia of a solid disk and sphere about their central axes.

1. Moment of Inertia
Concepts
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2. 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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3. 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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4. 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
through it
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5. 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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6. Example
Moment of Inertia of solid disk
about an central axis
2
2
1
MRI =
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7. Example
Moment of Inertia of
solid sphere around
central axis of Sphere
2
5
2
MRI =
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