Rotational Motion – Phase 1 (Page 2)

Previous IIT-JEE / JEE Main Problems (Moderate Level)

These problems are selected from previous papers and standard JEE patterns. They require concept + calculation + correct method.

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PYQ-7 (IIT-JEE)

A uniform disc of mass M and radius R rolls without slipping down an incline. Find the ratio of its translational kinetic energy to rotational kinetic energy.

Solution:

Translational KE = ½ Mv²
Rotational KE = ½ Iω²

For disc: I = ½ MR²
Rolling condition: v = ωR

Rotational KE = ½ × ½ MR² × (v²/R²) = ¼ Mv²

Ratio = (½ Mv²) : (¼ Mv²) = 2 : 1

Answer: 2 : 1

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PYQ-8 (JEE Main)

A particle moves in a circular path of radius r with speed v. Its angular momentum about the centre is:

Solution:

Angular momentum L = r × p

Here p = mv and r ⟂ v

So, L = mvr

Answer: mvr

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PYQ-9 (IIT-JEE)

A solid sphere and a solid cylinder of same mass and radius roll down an incline without slipping. Which reaches first?

Solution:

Acceleration for rolling body:
a = g sinθ / (1 + I/MR²)

Solid sphere: I = 2/5 MR² → denominator = 1 + 2/5 = 7/5
Solid cylinder: I = ½ MR² → denominator = 1 + ½ = 3/2

Smaller denominator ⇒ larger acceleration

Answer: Solid sphere reaches first

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PYQ-10 (AIEEE)

A torque τ acts on a body of moment of inertia I. The angular acceleration produced is:

Solution:

Newton’s second law for rotation:
τ = Iα

So, α = τ / I

Answer: α = τ / I

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PYQ-11 (JEE Main)

A wheel is rotating with angular velocity ω. If external torque is zero, which quantity remains constant?

Solution:

Using relation:
τ = dL/dt

τ = 0 ⇒ angular momentum remains constant

Answer: Angular momentum

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PYQ-12 (Board + JEE Pattern)

Why does a ring roll slower than a disc on an incline?

Solution:

Ring has larger moment of inertia:
I_ring = MR²
I_disc = ½ MR²

Larger I ⇒ smaller acceleration

Answer: Due to larger moment of inertia

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Exam Tips (Phase 1 – Page 2)

✔ Always write rolling condition v = ωR
✔ Compare I/MR² to decide speed
✔ Conservation laws reduce calculation
✔ Memorize standard moments of inertia

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Next: Phase 1 – Page 3 (Higher-Moderate IIT/JEE 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
• Phase 3 – Page 2
• Phase 3 – Page 3
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• Phase 3 – Page 5
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• Phase 3 – Page 7
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• 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
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• Phase 3 – Page 26
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• Phase 3 – Page 28
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• Phase 3 – Page 30
• Phase 3 – Page 31
• Phase 3 – Page 32
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• Phase 3 – Page 37
• Phase 3 – Page 38
• Phase 3 – Page 39

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