Rotational Motion (Class 11, Chapter 7 — Systems of Particles and Rotational Motion) is one of the most important and frequently tested chapters in JEE Main and JEE Advanced Physics, contributing 2–3 questions per paper. This guide covers moment of inertia, torque, angular momentum, rolling motion, and the key theorems you need to master for JEE 2027.
JEE Rotational Motion — Weightage
| Parameter | JEE Main | JEE Advanced |
|---|---|---|
| Avg. Questions | 2–3 | 3–5 |
| Difficulty | Medium | High |
| Class | 11 (Chapter 7) | 11 + extension |
| Marks potential | 8–12 | 12–20 |
Key Formulas — Rotational Motion
| Quantity | Formula | Linear Analogue |
|---|---|---|
| Angular velocity | u03c9 = du03b8/dt | v = dx/dt |
| Angular acceleration | u03b1 = du03c9/dt | a = dv/dt |
| Torque | u03c4 = r u00d7 F = Iu03b1 | F = ma |
| Angular Momentum | L = Iu03c9 = r u00d7 p | p = mv |
| Rotational KE | KE = u00bdIu03c9u00b2 | KE = u00bdmvu00b2 |
| Work by torque | W = u03c4u00b7u03b8 | W = Fu00b7d |
Moment of Inertia — Standard Results (Must Memorise)
| Body | Axis | I |
|---|---|---|
| Thin rod (length L) | Centre, perpendicular | MLu00b2/12 |
| Thin rod (length L) | End, perpendicular | MLu00b2/3 |
| Solid cylinder/disc (radius R) | Geometric axis | MRu00b2/2 |
| Hollow cylinder/ring (radius R) | Geometric axis | MRu00b2 |
| Solid sphere (radius R) | Diameter | 2MRu00b2/5 |
| Hollow sphere (radius R) | Diameter | 2MRu00b2/3 |
| Disc (radius R) | Diameter | MRu00b2/4 |
Parallel Axis Theorem and Perpendicular Axis Theorem
Parallel Axis Theorem
I = I_cm + Mdu00b2
I about any axis = I about parallel axis through CM + Mdu00b2, where d = distance between axes.
Perpendicular Axis Theorem (Laminar bodies only)
I_z = I_x + I_y
For flat (laminar) objects: MOI about axis perpendicular to plane = sum of MOI about two mutually perpendicular axes in the plane.
Conservation of Angular Momentum
When external torque = 0: L = Iu03c9 = constant
Classic examples:
- Skater pulling arms in u2192 I decreases u2192 u03c9 increases (L constant)
- Diver tucking u2192 I decreases u2192 rotates faster
- Earth’s orbit — angular momentum conserved (Kepler’s 2nd law)
Rolling Motion — JEE Favourite
For rolling without slipping: v = u03c9r (velocity of CM = angular velocity u00d7 radius)
Total KE = Translational KE + Rotational KE = u00bdmvu00b2 + u00bdIu03c9u00b2
Comparing Rolling Objects Down an Incline
| Object | I/MRu00b2 | Acceleration (a) | Reaches Bottom |
|---|---|---|---|
| Solid Sphere | 2/5 | 5g sinu03b8/7 | First |
| Solid Cylinder | 1/2 | 2g sinu03b8/3 | Second |
| Hollow Sphere | 2/3 | 3g sinu03b8/5 | Third |
| Ring/Hollow Cylinder | 1 | g sinu03b8/2 | Last |
Tip: Lower MOI u2192 higher acceleration u2192 reaches bottom first. Solid sphere always wins the race!
Practice Quiz — Rotational Motion JEE 2027
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FAQ
How to approach Rotational Motion in JEE Main?
Start with the linear-rotational analogy table — every linear concept has a rotational equivalent. Memorise the 6 standard MOI formulas cold. Then practice rolling motion problems (most common in JEE Main). Torque + angular momentum conservation problems appear in JEE Advanced.
Is Rotational Motion in JEE Advanced more difficult?
Yes. JEE Advanced tests rotational motion with multi-concept problems involving friction, torque, and energy simultaneously. Typical problems include a cylinder rolling on a rough incline, a rod falling from vertical, and systems with multiple rotating bodies. Practice 50+ problems after mastering concepts.
Practise these chapters on JEE Gurukul: start with the free 7-day demo, or see plans from ₹399 a month.