Chapter 6: Systems of Particles and Rotational Motion Class 11 Physics — summary, notes, extra questions & MCQ quiz

Summary

This chapter extends mechanics from a point particle to extended bodies, especially rigid bodies whose shape does not change. The centre of mass of a system is the mass-weighted average position, and it moves as if all the mass and the total external force were concentrated there, so its motion obeys Newton's laws even when individual particles move complexly. The total linear momentum of a system equals the total mass times the velocity of the centre of mass and is conserved when no external force acts. The vector (cross) product is introduced, leading to the definitions of torque \(\boldsymbol{\tau}=\mathbf{r}\times\mathbf{F}\) and angular momentum \(\mathbf{L}=\mathbf{r}\times\mathbf{p}\); the rotational analogue of Newton's second law is \(\boldsymbol{\tau}=\mathrm{d}\mathbf{L}/\mathrm{d}t\). When the net external torque is zero, angular momentum is conserved. A rigid body is in mechanical equilibrium when both net force and net torque vanish. The moment of inertia \(I=\sum m_ir_i^{2}\) is the rotational analogue of mass, depending on the mass distribution and axis; the radius of gyration and the theorems of perpendicular and parallel axes help compute it. Rotational kinematics mirrors linear kinematics with \(\theta,\omega,\alpha\), rotational kinetic energy is \(\tfrac12 I\omega^{2}\), and \(L=I\omega\) for rotation about a fixed axis.

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