Physics · Class 11 · Rotational Motion

Rotational Motion and Centre of Mass for JEE

Everything you need for this topic on one page: the ideas, the formulas, the traps, and free lectures that explain it well.

Last updated: 26 October 2026

Direct answer

Rotation is the hardest Class 11 mechanics chapter and appears in almost every paper: centre of mass, moment of inertia, torque, angular momentum and rolling.

Key ideas

Rotational Motion and Centre of Mass: what you must understand

Torque τ = r × F; τ = Iα about a fixed axis
Angular momentum is conserved when net external torque is zero
Rolling without slipping: v = ωR
Parallel and perpendicular axis theorems

Formula sheet

Must-know formulas for Rotational Motion and Centre of Mass

I_ring = MR², I_disc = ½MR², I_solid sphere = ⅖MR², I_rod (centre) = ML²/12
Parallel axis: I = I_cm + Md²
KE of rolling = ½mv²(1 + k²/R²)
Acceleration down incline (rolling) = g sinθ / (1 + k²/R²)

One-page formula sheet

Printable Rotational Motion and Centre of Mass formula sheet: formulas, key ideas and traps on one page. Save it as a PDF for offline revision.

Avoid

Common mistakes students make

Taking torque about a point that is accelerating
Forgetting static friction in rolling (it does no work but changes motion)
Mixing up I about the centre and about an edge

For the exam

How this topic is asked in JEE

Appears in almost every JEE Main shift. Learn the moment of inertia table cold. Most JEE Main rotation questions become one line after that.

Prerequisites: Laws of Motion and Friction, Work, Energy and Power.

NCERT map

Where Rotational Motion and Centre of Mass is in NCERT

Chapter names follow the current rationalised NCERT textbooks. Read these sections before solving PYQs.

Class	Book	Chapter	Sections JEE asks from
Class 11	Physics Part I	System of Particles and Rotational Motion	Centre of mass; Motion of centre of mass; Moment of inertia; Theorems of perpendicular and parallel axes; Torque and angular momentum; Rolling motion

JEE Advanced level

A JEE Advanced-level example on Rotational Motion and Centre of Mass

Question. A uniform solid cylinder of mass M = 4 kg and radius R = 0.2 m rests on a rough horizontal surface. A light inextensible string is wound around the cylinder and pulled horizontally with force F = 24 N, with the string leaving tangentially from the top of the cylinder. The cylinder rolls without slipping. Find (a) the acceleration of the centre of mass, and (b) the magnitude and direction of the friction force on the cylinder.

Show solution

Set up: Let acceleration of centre = a (in direction of F). For pure rolling, angular acceleration α = a/R. Let friction = f acting forward (same direction as motion, which can happen when force is applied above centre).
Translation equation: F + f = Ma gives 24 + f = 4a ... (1)
Rotation about centre: Torque by F (at top) = FR clockwise. Torque by f (at bottom) = fR anticlockwise. Net torque = FR − fR = Iα = (1/2)MR²(a/R) = (1/2)MRa. So F − f = (1/2)Ma gives 24 − f = 2a ... (2)
Solve (1) and (2): Adding gives 48 = 6a, so a = 8 m/s². From (2): f = 24 − 16 = 8 N.
Friction is positive, confirming it acts forward (in the direction of motion). This happens because the applied force at the top creates excess clockwise torque, and friction must act forward to maintain pure rolling.

Answer: (a) Acceleration = 8 m/s². (b) Friction = 8 N acting forward (in the direction of motion of the cylinder).

This example was solved twice independently and both solutions agree.

Free lectures

Best free lectures for Rotational Motion and Centre of Mass

Full-chapter free lectures picked from YouTube search results by views, from established JEE channels (mostly in Hinglish). Use the subtopic list to jump straight to the part you need (timestamps come from each video's own chapter list). Watch one, then solve PYQs the same day.

ROTATIONAL MOTION in One Shot: All Concepts & PYQs Covered || JEE Main & Advanced — JEE Wallah, 11:54:59
Jump to a subtopic (20)
- 00:00 Introduction
- 07:13 Rotation motion
- 21:15 Moment of inertia
- 1:00:15 MOI of body
- 1:47:24 Parallel and perpendicular axis theorem
- 2:47:56 Radius of gyration
- 3:32:31 Rotation effect
- 3:38:47 Torque
- 4:14:27 Equilibrium
- 4:59:32 Fix axis rotation
- 5:47:30 Work energy theorem
- 6:21:03 Pulley system
- 6:58:28 Angular momentum of a particle
- 8:32:20 Angular impulse
- 9:24:03 Combined Rotational Translation motion
- 9:47:25 Condition for rolling
- 10:16:30 Rolling on inclined plane
- 10:54:43 Angular momentum in CRTM
- 11:34:03 Toppling
- 11:54:55 Thank You Bachhon!
ROTATIONAL MOTION: Complete Chapter in 1 Video || All Concepts & PYQs Covered — PW JEE, 12:13:08

Practise

Where to practise for free

11 JEE Main 2026 PYQs on Rotational Motion and Centre of Mass, with solutions.
Read the chapter in NCERT textbooks (official, free), then solve its NCERT Exemplar (official, free) questions.
Chapter-wise past questions: JEE Main and Advanced PYQs and question bank.
Timed practice tests: NTA Abhyas practice tests (official, free) and our free mock tests.
See it move: interactive simulation.

FAQs

Frequently asked questions

Is Rotational Motion and Centre of Mass important for JEE Main 2027?

Appears in almost every JEE Main shift. It is part of the official 'Rotational Motion' unit in the JEE Main 2027 syllabus.

What are the most important formulas in Rotational Motion and Centre of Mass?

I_ring = MR², I_disc = ½MR², I_solid sphere = ⅖MR², I_rod (centre) = ML²/12; Parallel axis: I = I_cm + Md²; KE of rolling = ½mv²(1 + k²/R²).

How should I study Rotational Motion and Centre of Mass for JEE?

Understand the key ideas from NCERT or one full lecture, learn the formula sheet, then solve 25–30 past JEE questions on the topic. Learn the moment of inertia table cold. Most JEE Main rotation questions become one line after that.