Rotational Motion – Stage 1 (Page 4)

Angular Momentum & Rotational Equilibrium

Just like force is related to linear momentum, torque is related to angular momentum. This relationship is one of the most important ideas in rotational motion.

1. What is Angular Momentum?

Angular momentum of a particle about a point is defined as:

L = r × p

where
r = position vector
p = linear momentum (mv)

• SI unit: kg·m²·s⁻¹
• Vector quantity

2. Magnitude of Angular Momentum

|L| = r p sinθ

θ is the angle between r and p.

✔ Angular momentum depends on reference point
✔ Same particle can have different L about different points

3. Relation Between Torque & Angular Momentum

Net torque acting on a particle is equal to the rate of change of its angular momentum.

τ = dL / dt

This is the rotational analogue of:
F = dp / dt

4. Conservation of Angular Momentum

If net external torque acting on a system is zero, angular momentum remains constant.

Examples:
• Spinning skater pulling arms inward
• Planetary motion
• Rotating stool experiment

Exam Line: No external torque → L conserved.

5. Rotational Equilibrium

A rigid body is said to be in rotational equilibrium if the net torque acting on it is zero.

Condition: Στ = 0

This condition ensures:
✔ No angular acceleration
✔ Constant angular velocity (may be zero)

6. Complete Mechanical Equilibrium

For a body to be completely in equilibrium:

✔ Net force = 0 (translational equilibrium)
✔ Net torque = 0 (rotational equilibrium)

⚠ Common Mistakes

❌ Confusing torque with angular momentum ❌ Ignoring choice of reference point ❌ Applying L conservation when external torque exists

IIT-JEE Insight

IIT questions often hide the reference point. Choosing the correct point simplifies the problem greatly.

Next: Stage 1 – Page 5
Moment of Inertia – Concept, Definition & Physical Meaning

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