Rotational Motion – Phase 1 (Page 3)

Higher-Moderate IIT-JEE / JEE Main Problems (Solved)

These problems combine rolling + energy + torque + conservation laws. They are very common in JEE Main and older IIT-JEE papers.

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PYQ-13 (IIT-JEE)

A uniform disc rolls without slipping down an incline of height h. Find its speed at the bottom.

Solution:

Use conservation of energy:
Potential energy = Translational KE + Rotational KE

Mgh = ½Mv² + ½Iω²

For disc: I = ½MR²,   ω = v/R

Mgh = ½Mv² + ½ × ½MR² × (v²/R²)
Mgh = ½Mv² + ¼Mv² = ¾Mv²

v² = (4/3)gh ⇒ v = √(4gh/3)

Answer: v = √(4gh/3)

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PYQ-14 (JEE Main)

A rod of length L and mass M is hinged at one end and allowed to rotate freely from horizontal position. Find angular acceleration just after release.

Solution:

Torque about hinge:
τ = Mg × (L/2)

Moment of inertia about one end:
I = ML²/3

Using τ = Iα:

Mg(L/2) = (ML²/3)α

α = 3g / (2L)

Answer: α = 3g / (2L)

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PYQ-15 (IIT-JEE)

A disc is rotating freely. A small mass is gently placed on its rim. What happens to angular velocity?

Solution:

No external torque ⇒ angular momentum conserved

Initial: L_i = Iω Final: L_f = (I + mr²)ω'

Iω = (I + mr²)ω'

ω' < ω

Conclusion: Angular velocity decreases

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PYQ-16 (AIEEE)

A wheel rolls without slipping. If its centre moves with speed v, what is the kinetic energy of the wheel?

Solution:

Total KE = Translational KE + Rotational KE

KE = ½Mv² + ½Iω²

Using rolling condition: ω = v/R

Answer: KE = ½Mv² + ½I(v²/R²)

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PYQ-17 (JEE Main)

Why is a flywheel used in engines?

Solution:

Flywheel has large moment of inertia

⇒ Stores large rotational kinetic energy ⇒ Maintains uniform angular speed

Answer: To store energy and reduce speed fluctuations

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Phase-1 High-Scoring Strategy

✔ Prefer energy conservation over force equations
✔ Identify correct axis before using torque
✔ Write I clearly (half marks saver)
✔ Rolling ⇒ translation + rotation both

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Next: Phase 1 – Page 4 (Previous IIT-JEE Numerical Traps & Variations)

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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
• Phase 3 – Page 2
• Phase 3 – Page 3
• Phase 3 – Page 4
• Phase 3 – Page 5
• Phase 3 – Page 6
• Phase 3 – Page 7
• Phase 3 – Page 8
• Phase 3 – Page 9
• Phase 3 – Page 10
• Phase 3 – Page 11
• Phase 3 – Page 12
• Phase 3 – Page 13
• Phase 3 – Page 14
• Phase 3 – Page 15
• Phase 3 – Page 16
• Phase 3 – Page 17
• Phase 3 – Page 18
• Phase 3 – Page 19
• Phase 3 – Page 21
• Phase 3 – Page 22
• Phase 3 – Page 23
• Phase 3 – Page 24
• Phase 3 – Page 25
• Phase 3 – Page 26
• Phase 3 – Page 27
• Phase 3 – Page 28
• Phase 3 – Page 29
• Phase 3 – Page 30
• Phase 3 – Page 31
• Phase 3 – Page 32
• Phase 3 – Page 33
• Phase 3 – Page 34
• Phase 3 – Page 35
• Phase 3 – Page 36
• Phase 3 – Page 37
• Phase 3 – Page 38
• Phase 3 – Page 39

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