Rotational Motion is one of the top-3 JEE Physics chapters by weightage. Most questions become easy once you know the MOI table and treat rotation as the twin of linear motion.
Linear vs rotational
| Linear | Rotational |
|---|---|
| Mass m | Moment of inertia I |
| Force F = ma | Torque τ = Iα |
| Momentum p = mv | Angular momentum L = Iω |
| KE = ½mv² | KE = ½Iω² |
| v = u + at | ω = ω₀ + αt |
MOI table (mass M)
| Body | Axis | I |
|---|---|---|
| Ring, radius R | Centre, ⊥ plane | MR² |
| Disc | Centre, ⊥ plane | ½MR² |
| Solid sphere | Diameter | (2/5)MR² |
| Hollow sphere | Diameter | (2/3)MR² |
| Rod, length L | Centre, ⊥ | ML²/12 |
| Rod | End, ⊥ | ML²/3 |
| Solid cylinder | Axis | ½MR² |
| Rectangular plate a × b | Centre, ⊥ | M(a² + b²)/12 |
Theorems
- Parallel axis: I = Icm + Md²
- Perpendicular axis (laminas): Iz = Ix + Iy → disc about diameter = ¼MR²
- Radius of gyration k: I = Mk²
Rolling without slipping
- vcm = ωR; KE = ½mv²(1 + k²/R²)
- On an incline: a = g sin θ/(1 + k²/R²) — sphere (2/5) beats disc (1/2) beats ring (1)
- Minimum friction for rolling: μ ≥ tan θ/(1 + R²/k²)
Solved
1. Solid sphere rolling down a 30° incline: a = g sin30/(1 + 2/5) = 5/1.4 = 3.57 m/s².
2. Angular momentum conservation: a dancer pulls in arms, I halves → ω doubles, KE doubles (work done by muscles).
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3. Torque on a rod pivoted at one end released horizontally: α = τ/I = (MgL/2)/(ML²/3) = 3g/2L.
Common mistakes
- Using ½MR² for a ring
- Applying the perpendicular axis theorem to 3D bodies
- Forgetting rotational KE in energy conservation for rolling
Related: Laws of Motion Class 11.
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Frequently asked questions
Is this Rotational Motion content at JEE/NEET level?
Yes. It covers the formulas, facts and question types that appear in JEE Main, JEE Advanced and NEET, with the NCERT base that these exams follow.
How many questions come from Rotational Motion?
Typically one to three questions per paper, depending on the year. Check the chapter-wise weightage post and give this topic time in proportion.
Where can I get rotational motion doubts solved quickly?
On DoubtPay AI you can type or photograph a module or mock-test question, select JEE or NEET, and get a step-by-step solution, a hint, or a check of your own attempt in seconds. ₹49 gives 100 answers with no subscription.
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