Rotational Motion – Phase 2 (Page 8)

Extreme IIT-JEE Advanced Problems (Rank Booster)

These problems appear simple but are conceptually brutal. They test axis choice, impulse torque, constraints, and conservation laws.

TP-11 (IIT-JEE Advanced)

A uniform disc of mass M and radius R rests on a smooth horizontal surface. A horizontal impulse J is applied at its rim. Find the velocity of the centre of mass immediately after the impulse.

Key Insight:

Surface is smooth ⇒ no external horizontal force after impulse.
Impulse provides:

Linear impulse → linear momentum
Angular impulse → angular momentum

Linear momentum:
Mv = J ⇒ v = J / M

Answer: v = J / M

Trap: Many students wrongly assume part of impulse goes into rotation.

TP-12 (IIT-JEE Advanced)

A disc is rotating freely with angular speed ω. Suddenly a small hole is drilled at the centre. What happens to angular velocity?

Thinking:

Removing mass at centre ⇒ no change in moment of inertia.
No external torque.

Answer: Angular velocity remains unchanged.

Trap: Assuming every mass removal changes angular speed.

TP-13 (IIT-JEE Advanced)

A disc rolls without slipping on rough ground. Suddenly the ground becomes smooth. What happens to:
(a) Angular velocity
(b) Linear velocity?

Logic:

On smooth ground ⇒ friction = 0 ⇒ no torque.

Angular velocity ⇒ remains constant
Linear velocity ⇒ remains constant

Answer: Both remain unchanged.

TP-14 (IIT-JEE Advanced)

A uniform rod of length L is rotating in horizontal plane about its centre. Two equal impulses J are applied simultaneously at its ends in opposite directions. Find angular velocity produced.

Solution:

Net linear impulse = 0 ⇒ no translation.

Net angular impulse:
τΔt = J(L/2) + J(L/2) = JL

Moment of inertia about centre:
I = ML² / 12

ω = (JL) / (ML²/12)

Answer: ω = 12J / (ML)

TP-15 (IIT-JEE Advanced – Conceptual)

Can a body have zero angular momentum and non-zero angular velocity?

Explanation:

Yes.
Angular momentum depends on reference point.

Example: Two equal masses rotating oppositely about centre.

Answer: Yes, depending on reference axis.

EXTREME-LEVEL THINKING RULES (Memorize)

✔ Always ask: Which axis?
✔ Sudden event → use impulse & angular impulse
✔ Smooth surface ⇒ no torque
✔ Angular momentum survives when linear momentum fails
✔ Mass removal/addition → check where it occurs

Next: Phase 3 – Exam Mastery (Tricks, Traps, Topper Thinking)

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🔄 Rotational Motion – Phase 3 (Exam Mastery Series)

Advanced exam-oriented thinking series focusing on traps, execution, pressure handling, and topper strategies.

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