Rotational Motion – Stage 1 (Page 9)

Rotational Dynamics & Equation τ = Iα

Rotational dynamics studies the relation between torque, moment of inertia, and angular acceleration. It is the rotational analogue of Newton’s second law.

1. Newton’s Second Law for Rotation

The net external torque acting on a rigid body is equal to the product of its moment of inertia and angular acceleration.

τ = I α

where
τ = net torque
I = moment of inertia
α = angular acceleration

2. Physical Meaning of τ = Iα

✔ Larger torque → larger angular acceleration
✔ Larger moment of inertia → smaller angular acceleration
✔ Rotation depends on axis through I

This explains why heavier flywheels rotate slowly even under large torque.

3. Linear vs Rotational Dynamics (Very Important)

Force (F) ↔ Torque (τ)
Mass (m) ↔ Moment of inertia (I)
Acceleration (a) ↔ Angular acceleration (α)
F = ma ↔ τ = Iα

4. Multiple Torques Acting on a Body

When more than one torque acts on a body, we must consider the net torque.

τ_net = τ₁ + τ₂ + τ₃ + …

Use sign convention:
• Anticlockwise → positive
• Clockwise → negative

5. Applications of τ = Iα

✔ Rotating pulleys
✔ Rolling objects on inclines
✔ Flywheels and gears
✔ Disc and ring acceleration problems

⚠ Common Student Mistakes

❌ Using wrong moment of inertia ❌ Forgetting direction of torque ❌ Ignoring net torque concept

IIT-JEE Insight

IIT problems often combine τ = Iα with energy conservation or rolling conditions. Understanding this equation deeply saves time.

Next: Stage 1 – Page 10
Rolling Motion, No-Slipping Condition & Combined Dynamics

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