The moment of inertia of thin disc of mass m and radius r, about an axis passing through one of its diameter is given by

 Moment of inertia is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation. Or in more simple terms, it can be described as a quantity that decides the amount of torque needed for a specific angular acceleration in a rotational axis.

The moment of inertia depends on the following factors,

  • The density of the material
  • Shape and size of the body
  • Axis of rotation (distribution of mass relative to the axis)

We know that moment of inertia of disk about A1(I1)=MR2/2

Applying Perpendicular theorem,

I1=I2 + I3

MR2/2 = I2 + I3

By the symmetry of disk, we can conclude that

I= I3

So, MR2/2 = 2I2

⇒ I2 = I3 = MR2/4

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