Rotational Motion – Stage 1 (Page 5)

Moment of Inertia – The Rotational Mass

In linear motion, mass resists change in velocity. In rotational motion, moment of inertia resists change in angular velocity.

Moment of inertia tells us how difficult it is to rotate a body about a given axis.

1. What is Moment of Inertia?

Moment of inertia of a particle about a given axis is defined as:

I = m r²

where
m = mass of the particle
r = perpendicular distance from axis of rotation

• SI unit: kg·m²
• Scalar quantity

2. Moment of Inertia of a System of Particles

For a system of particles:

I = Σ mᵢ rᵢ²

Each particle contributes independently to total moment of inertia.

3. Physical Meaning of Moment of Inertia

✔ More mass → more inertia
✔ Mass farther from axis → much larger inertia
✔ Axis of rotation is crucial

This explains why:
• A hollow cylinder rolls slower than a solid one
• Tight-rope walkers extend arms for balance

4. Dependence of Moment of Inertia

Moment of inertia depends on:

✔ Mass of body
✔ Distribution of mass
✔ Axis of rotation

Important: Same body → different I for different axes.

5. Comparison with Mass (Very Important)

Mass → resistance to linear acceleration
Moment of inertia → resistance to angular acceleration

Linear: F = m a
Rotational: τ = I α

⚠ Common Student Mistakes

❌ Treating moment of inertia as constant like mass ❌ Forgetting axis dependence ❌ Using radius instead of perpendicular distance

IIT-JEE Insight

In IIT problems, choosing the correct axis can reduce calculations by half. Always identify the axis first.

Next: Stage 1 – Page 6
Radius of Gyration & Standard Moments of Inertia

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