Ch 7 extends mechanics to systems of particles and rigid body rotation. Students learn centre of mass, torque, moment of inertia, angular momentum conservation, and rolling motion.
Centre of mass: effective point where total mass acts. R_cm = Σm_i r_i / M. For symmetric bodies, COM is at geometric centre. Torque: τ = r × F (rotational equivalent of force). A body is in equilibrium when net force and net torque are both zero.
Moment of inertia I = Σm_i r_i² (rotational equivalent of mass). Depends on mass distribution and axis. Parallel axis theorem: I = I_cm + Md². Perpendicular axis theorem (lamina): I_z = I_x + I_y. Newton's 2nd law for rotation: τ = Iα. Angular momentum L = Iω. Conservation: if τ_net = 0, L = constant (ice skater spinning).
Download: https://ncert.nic.in/textbook/pdf/keph107.pdf | Part I: https://ncert.nic.in/textbook/pdf/keph1ps.zip
For a rolling body, acceleration down an incline is a = g sinθ / (1 + I/MR²). For a ring, I = MR², so a = g sinθ/2. For a disc, I = ½MR², so a = 2g sinθ/3. The disc has greater acceleration and reaches the bottom first because a larger fraction of its gravitational PE converts to translational KE (less goes to rotation).
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