Chapter 6 — Systems of Particles and Rotational Motion

Chapter 6 of the Class 11 Physics NCERT textbook, "System of Particles and Rotational Motion", covers systems of particles, rotational motion, centre of mass, torque, angular momentum, and moment of inertia. The free NCERT PDF is available to download.

• Extended bodies and centre of mass — Real objects are not points, so the chapter analyses rigid bodies through the centre of mass—the balance point where the total gravitational torque vanishes—allowing an extended body's overall motion to be treated compactly.
• Rotational analogues of linear motion — Each linear quantity has a rotational counterpart: moment of inertia plays the role of mass, torque the role of force, and angular momentum the role of momentum, all governed by rotational versions of Newton's second law.
• Equilibrium and combined motion — The chapter distinguishes pure translation, pure rotation, and combined motion, and sets the conditions for a rigid body to stay in equilibrium. Angular momentum conservation under zero external torque unifies these cases.

1. 01Centre of mass is defined by R = Σ(m_i r_i)/M; for symmetric bodies it coincides with the geometric centre.
2. 02Linear velocity and angular velocity are related by v = ω × r, where ω is the angular velocity vector along the axis of rotation.
3. 03Moment of inertia I = Σ(m_i r_i²) is the rotational analogue of mass; kinetic energy of rotation is K = (1/2)Iω².
4. 04Torque τ = r × F and angular momentum L = r × p obey the rotational analogue of Newton's second law: τ = Iα and dL/dt = τ_ext.
5. 05A rigid body in mechanical equilibrium must satisfy: (1) ΣF = 0 (translational) and (2) Στ = 0 (rotational).
6. 06For rotation about a fixed axis with no external torque, angular momentum is conserved: L = Iω = constant.