ঘূর্ণন গতি ও জড়তা ভ্রামক
Center of mass integration, torque cross-product, angular momentum conservation, moment of inertia theorems, and pure rolling.
Center of mass coordinates for discrete and continuous mass distributions, velocity and acceleration of CM, and internal forces.
Torque vector cross product τ = r × F, angular momentum L = r × p, torque as dL/dt, and conservation of angular momentum.
Derivations for center of mass of continuous bodies, parallel/perpendicular axis theorem proofs, and rotational kinetic energy.
Physical significance of moment of inertia, radius of gyration, parallel axis theorem I = I_cm + Md^2, perpendicular axis theorem I_z = I_x + I_y.
Equations of rotational motion with constant angular acceleration, rotational kinetic energy 1/2 I ω^2, and rotational power P = τ · ω.
Pure rolling kinematics v_cm = Rω, total kinetic energy K = 1/2 M v^2 (1 + k^2/R^2), acceleration of rolling bodies down an inclined plane.