Chapter 6 — Systems of Particles and Rotational Motion

The NCERT Class 11 Physics Chapter 6 PDF is free to download directly from the NCERT website. It covers systems of particles, rotational motion, centre of mass, torque, angular momentum, and moment of inertia.

Chapter 6 teaches how to analyze the motion of extended bodies (rigid bodies) using the concepts of centre of mass, torque, and rotational dynamics. Key topics include the centre of mass as the point where total gravitational torque is zero, the relationship between linear and angular motion via the vector product (v = ω × r), moment of inertia as the rotational analogue of mass, and the fundamental equation τ = Iα. The chapter distinguishes pure translation, pure rotation about a fixed axis, and combined motion, using symmetry arguments and vector formulations to solve problems involving equilibrium, levers, conservation of angular momentum, and rotational kinematics.

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.