NCERT Notes Class 11 Physics Chapter 6 System of Particles and Rotational Motion

These Class 11 Physics Notes Chapter 6 System of Particles and Rotational Motion pull together every centre-of-mass rule, torque and angular-momentum relation, moment-of-inertia value, and rolling-motion formula that the Boards, JEE Main, JEE Advanced, NEET, CUET and NDA papers actually test in 2026-27. Use them to revise the whole chapter fast, with formulas, definitions and derivations in one place.

This chapter is the bridge from point-particle mechanics to real extended bodies, and its ideas return in gravitation, oscillations and every rotation numerical you meet later.

• CBSE Weightage: 6 to 8 marks, usually one short answer plus one long numerical on torque, moment of inertia or rolling.
• Topics covered: centre of mass, torque, angular momentum, its conservation, moment of inertia, radius of gyration, the two axis theorems, rolling motion and equilibrium.
• Key formulas: τ = Iα, L = Iω, the parallel and perpendicular axes theorems, and rolling kinetic energy.

These Class 11 Physics Notes Chapter 6 System of Particles and Rotational Motion are curated by subject experts, based on the 2026-27 NCERT textbook, and checked against the last five years of CBSE Board, JEE Main and NEET papers.

Topic-by-Topic Summary of System of Particles and Rotational Motion

The chapter moves from a system of many particles to a spinning rigid body. It starts with the centre of mass, then builds torque and angular momentum as the rotational partners of force and linear momentum. Here is the quick map of what each topic gives you.

• Centre of mass: the single point that moves as if all the mass and the total external force acted there.
• Torque and angular momentum: the turning effect of a force, and the rotational version of momentum.
• Conservation of angular momentum: when no external torque acts, spin momentum stays fixed.
• Moment of inertia and radius of gyration: how mass spread around an axis resists rotation.
• Axis theorems and rolling: the parallel and perpendicular axes theorems, plus rolling without slipping.

Revise the topics in this order, because each one uses the one before it. Master torque and moment of inertia first, and the rest of the numericals fall into place. These Class 11 Physics Notes Chapter 6 System of Particles and Rotational Motion follow the same sequence as the NCERT textbook.

Centre of Mass and Its Motion

The centre of mass is the single point where the whole mass of a body or system can be taken to act. When an external force is applied, the centre of mass moves as if all the mass were concentrated there. This idea lets you treat a complicated body as one particle.

• Position: for particles of mass m_i at r_i, the centre of mass is R = (Σ m_ir_i)/M.
• Velocity: MV = Σ m_iv_i, which equals the total linear momentum of the system.
• Motion: the centre of mass obeys F_ext = Ma_cm, so internal forces never change its path.

The total momentum of a system equals its total mass times the velocity of the centre of mass. This is why a spinning cracker that bursts still has its centre of mass follow the original parabola. For symmetric uniform bodies the centre of mass sits at the geometric centre, which saves time in the exam.

Torque and Angular Momentum of a Rigid Body

Torque is the turning effect of a force about an axis, and angular momentum is the rotational partner of linear momentum. These two quantities drive every rotation problem in the chapter, so learn their vector forms and their magnitudes.

• Torque: τ = r × F, with magnitude τ = rF sinθ. Its SI unit is the newton metre.
• Angular momentum: L = r × p, with magnitude L = mvr sinθ.
• Link between them: τ = dL/dt, the rotational form of Newton's second law.

For a rigid body turning about a fixed axis, these become L = Iω and τ = Iα, where I is the moment of inertia. Torque plays the role of force, and moment of inertia plays the role of mass, in rotation. Keeping this force-to-torque map in mind makes the whole chapter easier to remember.

Conservation of Angular Momentum and Its Applications

When the net external torque on a system is zero, its angular momentum stays constant. This is one of the most tested ideas of the chapter, because it explains everyday spinning and appears in both Boards and entrance papers.

• Statement: if τ_ext = 0, then L = Iω = constant.
• Skater example: a skater pulls in the arms, I falls, so ω rises to keep Iω fixed.
• Diver example: a diver curls up to spin faster, then opens out to slow the spin before entering the water.

A fall in moment of inertia forces a rise in angular speed when angular momentum is conserved. Write the conservation equation I₁ω₁ = I₂ω₂ on its own line in numericals. Markers award the method mark for stating conservation before you plug in numbers.

Moment of Inertia and Radius of Gyration

The moment of inertia measures how hard it is to change a body's rotation. It depends not just on mass but on how that mass is spread around the axis. The radius of gyration repackages this as a single distance.

• Definition: I = Σ m_ir_i², the sum of each mass times its squared distance from the axis.
• Radius of gyration: I = MK², so K = √(I/M).
• Meaning: K is the distance from the axis at which the whole mass could sit to give the same moment of inertia.

Standard values are asked directly, so memorise them. A ring about its central axis has I = MR², a disc has ½ MR², and a solid sphere has (2/5) MR². Moment of inertia grows when mass sits farther from the axis, even if the total mass is unchanged.

Parallel and Perpendicular Axes Theorems

These two theorems let you find the moment of inertia about a new axis without redoing the whole sum. They are short to state, quick to apply, and appear almost every year in some form.

The parallel axes theorem works for any body, but the perpendicular axes theorem holds only for a flat lamina. Mixing up where each one applies is a frequent slip. Use the parallel axes theorem to shift an axis, and the perpendicular axes theorem to relate three axes of a thin plate.

All Formulas for System of Particles and Rotational Motion

Every formula you need for the chapter sits in one table below, with its meaning and its SI unit. Learn the torque, angular-momentum and rolling rows first, since those carry the most marks in both Boards and entrance papers.

Carry the SI unit on every line of your working. Losing the unit is a silent way to drop the final mark even when the number is right. Keep this table open while you solve the back-exercise numericals.

Key Definitions and Derivations for System of Particles and Rotational Motion

Boards short-answer questions often ask for a clean definition in one or two lines. Learn these word-for-word, because a vague definition loses easy marks. Each one also sets up a derivation you can be asked to show.

A common derivation asks you to relate torque and angular acceleration. Start from L = Iω and differentiate to reach τ = Iα, treating the moment of inertia as constant. Another favourite is proving that the total external torque equals the rate of change of the system's angular momentum.

Rolling Motion and Equilibrium of a Rigid Body

The chapter closes with two applied topics that carry easy marks. Rolling motion combines translation and rotation, while equilibrium sets the conditions for a body to stay at rest. Both appear as short answers and numericals.

• Rolling condition: for rolling without slipping, v_cm = Rω, so the contact point is momentarily at rest.
• Rolling energy: total kinetic energy is ½ Mv²(1 + K²/R²), splitting into translation plus rotation.
• Equilibrium: a rigid body is in equilibrium when both ΣF = 0 and Στ = 0.

A body needs zero net force and zero net torque to be in complete equilibrium. On an incline, a hollow shape rolls down slower than a solid one because more of its mass sits far from the axis, giving a larger K²/R². This single fact answers many objective questions for JEE Main and NEET.

Common Mistakes Students Make in System of Particles and Rotational Motion

These slips happen while writing or calculating, not because the concept is unclear. Each one costs 1 to 3 marks in the paper, so watch for them at the exact step.

System of Particles and Rotational Motion Weightage in CBSE Boards, JEE and NEET

This chapter is a reliable scorer. It usually carries one short answer plus one full numerical, and it feeds objective questions in every entrance paper. Here is how the marks split across the main exams for 2026-27.

Moment of inertia and rolling motion are the single most tested ideas from this chapter across all four exams. Master them first, then torque and angular momentum, then the centre of mass, in that order of return on effort.

How to Revise System of Particles and Rotational Motion Quickly

Use these Class 11 Physics Notes Chapter 6 System of Particles and Rotational Motion for a fast, ordered recap the night before a test. The checklist below takes about 30 minutes and hits every marks-heavy idea.

• First 10 minutes: write the moment of inertia of a ring, disc, rod and solid sphere from memory, with the axis stated.
• Next 10 minutes: redo one torque numerical and one conservation-of-angular-momentum numerical.
• Last 10 minutes: apply the parallel and perpendicular axes theorems once each, then check a rolling kinetic-energy problem.

Close the loop by stating both equilibrium conditions from memory. If you can do all three blocks without notes, the chapter is exam-ready. Keep the All Formulas table beside you for the first pass only, then try it closed-book.

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