Rotational Motion – Phase 2 (Page 7)
Ultra-Tough IIT-JEE Advanced Problems (Multi-Concept)
These problems test true rotational mastery. You must combine collision, rolling, angular momentum, energy.
TP-6 (IIT-JEE Advanced)
A disc of mass M and radius R is initially at rest on a rough horizontal surface. A particle of mass m moving with velocity v hits the rim tangentially and sticks. Find the velocity of the centre just after collision.
Solution:
External impulse in horizontal direction exists ⇒ linear momentum NOT conserved.
But torque about centre is zero ⇒ angular momentum conserved.
Initial angular momentum:
Li = m v R
Final moment of inertia:
I = ½MR² + mR²
Angular velocity:
ω = (m v R) / (½MR² + mR²)
Velocity of centre:
vcm = ωR
Answer: vcm = (m v) / (M/2 + m)
TP-7 (IIT-JEE)
A uniform rod of mass M and length L rests on a smooth horizontal surface. It is given an impulse at one end perpendicular to its length. Find angular velocity of the rod.
Solution:
Impulse J gives:
Linear momentum = J
Angular impulse about centre:
L = J × (L/2)
Moment of inertia about centre:
I = ML²/12
Angular velocity:
ω = (J L / 2) / (ML²/12)
Answer: ω = 6J / (ML)
TP-8 (JEE Advanced)
A sphere rolls down an incline and then moves on a smooth surface. Which quantity changes suddenly at the junction?
Logic:
On incline: rolling ⇒ both translation + rotation
On smooth surface: no friction ⇒ no torque
Answer: Angular acceleration becomes zero suddenly
TP-9 (IIT-JEE Advanced)
A disc rolls without slipping and suddenly enters a smooth surface. What happens to its angular velocity?
Solution:
No friction ⇒ no torque ⇒ angular velocity remains constant
Answer: Angular velocity remains unchanged
TP-10 (IIT-JEE Advanced – Trap)
A rotating body has zero angular momentum. Can it still be rotating?
Explanation:
Angular momentum depends on reference point.
Yes, it can rotate and still have L = 0 about some axis.
Answer: Yes (depends on reference axis)
IIT-LEVEL THINKING RULES
✔ Always check which conservation law applies
✔ Linear momentum often fails, angular momentum survives
✔ Axis selection decides everything
✔ Sudden changes → check impulses & torques
✔ Do NOT assume rolling everywhere
Next: Phase 2 – Page 8 (Extreme JEE Advanced Problems + Traps)
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