Moment of inertia of a uniform circular disc about a...

Moment of inertia of a uniform circular disc about a diameter is $I$. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be
(a) 51
(b) 31
(c) 61
(d) $4 \overline{1}$

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Key Concepts

Parallel Axis Theorem

Also known as Steiner’s theorem, this theorem is used to calculate the moment of inertia of a body about any axis parallel to an axis through its center of mass. It shows that the moment of inertia about any parallel axis is equal to the moment of inertia about the center of mass plus the product of the body’s mass and the square of the distance between the two axes. This is critical when shifting the axis of rotation from a central axis to one that is offset, such as through a point on the rim of a disc.

Perpendicular Axis Theorem

This theorem applies to planar objects and states that the moment of inertia about an axis perpendicular to the plane of the object is equal to the sum of the moments of inertia about two mutually perpendicular axes lying in the plane and intersecting at a point. It is particularly useful for calculating the moment of inertia for flat bodies, leveraging known moments about in-plane axes.

Moment of Inertia

It is a physical quantity that measures the rotational inertia of an object, reflecting how mass is distributed relative to a chosen axis of rotation. In problems involving rigid bodies, the moment of inertia plays a role analogous to mass in linear motion, affecting the resistance to angular acceleration and determining the dynamic behavior of the system.

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