What are the factors on which moment of inertia of a body depend.

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Accepted Answer

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> [!TLDR]
> I depends on mass, distribution of mass about the axis, and the position of the axis.
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> Moment of inertia $I = \sum m_i r_i^2$ measures a body's resistance to change in its rotational motion, playing the same role as mass in linear motion. From this definition, $I$ depends on:
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> 1. **Mass of the body** — larger mass gives larger $I$.
> 2. **Distribution of mass about the axis** — mass concentrated farther from the axis contributes more (the $r_i^2$ term), so the same mass arranged differently gives a different $I$.
> 3. **Shape and size of the body** — a ring and a disc of the same mass and radius have different $I$ because their mass is distributed differently. …

Linear Quantity	Rotational Analogue
Displacement $x$	Angular displacement $\theta$
Velocity $v$	Angular velocity $\omega$
Acceleration $a$	Angular acceleration $\alpha$
Mass $m$	Moment of inertia $I$
Force $F$	Torque $\tau$
Newton's 2nd law: $F = ma$	$\tau = I\alpha$
Kinetic energy: $\frac{1}{2}mv^2$	$\frac{1}{2}I\omega^2$
Momentum: $p = mv$	Angular momentum: $L = I\omega$

Q.What are the factors on which moment of inertia of a body depend.

Concept understanding — Rotational Dynamics

Rotational Dynamics: The Physics of Spinning Things

The Core Idea

Breaking It Down

Torque — The Rotational "Push"

Moment of Inertia — The Rotational "Mass"

Angular Acceleration — How Fast Rotation Changes

The Complete Picture: Rotational Analogues

The Key Insight: Conservation of Angular Momentum

Q.What are the factors on which moment of inertia of a body depend.

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