Schooling · Class 11 · Physics · System of Particles and Rotational Motion · Chapter on a page
CBSE Class 11 · Physics · NCERT Physics Part-I
System of Particles and Rotational Motion: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 27 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- Centre of mass (CM)
- Motion of the CM
- Torque (τ)
- Moment of inertia (I)
- Angular momentum (L)
- Rotational Newton's second law
- Conservation of angular momentum
- Formulas and facts
- x_cm = Σ mᵢxᵢ / Σ mᵢ
- τ = r F sin θ
- I = Σ mᵢrᵢ²
- I_parallel = I_cm + Md²
- L = Iω
- τ = Iα
- KE_rot = ½ Iω²
- Worked examples
- Finding the centre of mass
- Torque on a door
- Angular momentum conservation
- Watch out for
- Confusing torque with force
- Using the wrong axis for moment of…
- Forgetting that rolling has both…
- Applying conservation of angular…
- Treating moment of inertia as a…
What this chapter is about
Until now, you have treated objects as point masses — their entire mass concentrated at a single point. This chapter extends mechanics to extended bodies, objects with finite size and shape. When a cricket bat swings, a fan rotates, or a potter's wheel spins, different parts of the object move differently. Understanding such motion requires new concepts: the centre of mass, torque, angular momentum and moment of inertia.
Key ideas
- Centre of mass (CM): The point where the entire mass of a system can be thought to be concentrated for analysing its translational motion. For two particles of masses m₁ and m₂ at positions x₁ and x₂, the CM is at x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂).
- Motion of the CM: The CM of a system moves as though all external forces act on a point mass equal to the total mass located there. Internal forces do not affect the CM's motion.
- Torque (τ): The rotational analogue of force. For a force F applied at position r from the axis, τ = r × F. Its magnitude is τ = rF sin θ, where θ is the angle between r and F. SI unit: N m.
- Moment of inertia (I): The rotational analogue of mass. It measures how mass is distributed about the axis. For discrete particles, I = Σ mᵢrᵢ². SI unit: kg m².
- Angular momentum (L): The rotational analogue of linear momentum. For a particle, L = r × p. For a rigid body rotating about a fixed axis, L = Iω. SI unit: kg m²/s.
- Rotational Newton's second law: Net external torque equals rate of change of angular momentum. τ_net = dL/dt. For a rigid body with constant I, τ_net = Iα, where α is angular acceleration.
- Conservation of angular momentum: If net external torque on a system is zero, its total angular momentum remains constant.
- Rolling motion: Combines rotation about the CM and translation of the CM. For rolling without slipping, v_cm = Rω, where R is the radius.
Formulas and facts to remember
- Formula: x_cm = Σ mᵢxᵢ / Σ mᵢ · Meaning: x-coordinate of centre of mass
- Formula: τ = r F sin θ · Meaning: Magnitude of torque
- Formula: I = Σ mᵢrᵢ² · Meaning: Moment of inertia of discrete particles
- Formula: I_parallel = I_cm + Md² · Meaning: Parallel-axis theorem: I about any axis equals I about a parallel axis through CM plus Md²
- Formula: L = Iω · Meaning: Angular momentum of a rotating rigid body
- Formula: τ = Iα · Meaning: Newton's second law for rotation (constant I)
- Formula: KE_rot = ½ Iω² · Meaning: Rotational kinetic energy
- Formula: KE_total (rolling) = ½ Mv_cm² + ½ I_cm ω² · Meaning: Total kinetic energy in rolling motion
- Formula: v_cm = Rω (no slipping) · Meaning: Condition for pure rolling
- Moment of inertia for common shapes (about axis through CM):
- Thin rod about centre, perpendicular to length: I = (1/12)ML²
- Solid sphere about diameter: I = (2/5)MR²
- Solid disc about axis through centre, perpendicular to plane: I = (1/2)MR²
- Hollow sphere about diameter: I = (2/3)MR²
Common mistakes
- Confusing torque with force → Torque depends on where and at what angle the force is applied; always include r and sin θ.
- Using the wrong axis for moment of inertia → I changes with axis; apply the parallel-axis theorem when the axis is not through the CM.
- Forgetting that rolling has both translational and rotational KE → Include ½ Mv_cm² and ½ I_cm ω² when energy methods are used.
- Applying conservation of angular momentum when external torque exists → First check that net external torque about the chosen axis is zero.
- Treating moment of inertia as a single number for all axes → I is axis-specific; a rod has different I about its centre and about its end.
Quick revision
- Centre of mass is the mass-weighted average position; it moves as if all external forces act there.
- Torque = r × F; it causes angular acceleration, not linear acceleration.
- Moment of inertia depends on mass distribution and the chosen axis.
- τ = Iα is the rotational analogue of F = ma.
- When net external torque is zero, angular momentum L = Iω is conserved.
- For pure rolling without slipping, v_cm = Rω.