Rotational Motion – Phase 1 (Page 5)

Mixed Numericals + Speed Solving Tricks

This page combines rolling motion, energy, torque, and angular momentum. Each problem includes a fast approach used by toppers.

PYQ-23 (JEE Main)

A solid cylinder of mass M and radius R rolls without slipping with speed v. Find its total kinetic energy.

Fast Method:

Total KE = Translational KE + Rotational KE

= ½Mv² + ½Iω²

For solid cylinder: I = ½MR², ω = v/R

KE = ½Mv² + ¼Mv² = ¾Mv²

Answer: ¾Mv²

PYQ-24 (IIT-JEE)

A disc and a ring roll down an incline of same height. Find ratio of their speeds at bottom.

Shortcut:

Use energy conservation:
v² ∝ 1 / (1 + I/MR²)

Disc: I/MR² = ½
Ring: I/MR² = 1

v_disc : v_ring = √(2/3) : √(1/2)

Result: Disc reaches faster

PYQ-25 (JEE Main)

A wheel starts rolling from rest without slipping. Which force is responsible for angular acceleration?

Concept:

Static friction provides torque about centre.

Answer: Static friction

PYQ-26 (IIT-JEE)

A rotating disc suddenly breaks into two equal parts. What happens to angular velocity?

Method:

Check external torque → zero
Apply angular momentum conservation.

Since I decreases → ω increases.

Conclusion: Angular velocity increases

PYQ-27 (JEE Main)

Why is angular velocity maximum at centre when a man moves inward on a rotating platform?

Fast Explanation:

No external torque → L = Iω = constant

I decreases → ω increases

Answer: Due to conservation of angular momentum

TOPPER SPEED TRICKS (Very Important)

✔ Prefer energy over force equations
✔ Compare I/MR², not I directly
✔ Rolling ⇒ write v = ωR immediately
✔ No torque ⇒ angular momentum conserved
✔ Memorize KE fractions for disc, ring, sphere

COMMON TIME-WASTERS

❌ Writing full force equations unnecessarily
❌ Forgetting axis of rotation
❌ Ignoring rotational KE
❌ Over-calculating simple ratios

Phase 1 COMPLETED ✅
Next: Phase 2 – IIT/JEE Tough Problems

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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.

Phase 3 – Page 1
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