CONCEPT MAP

The unit's concept map traces the logical spine of the whole chapter. It begins with the rigid body idealisation and its center of mass — the single point standing in for the whole body's translational motion, located by the mass-weighted position formula and, for two point masses, obeying the principle of moments. From there the map branches on the idea of torque, $\vec\tau=\vec r\times\vec F$, and its rotational partner angular momentum, $\vec L=\vec r\times\vec p=I\omega$, related by $\tau=dL/dt$.

One branch develops equilibrium of rigid bodies: the net-force-zero and net-torque-zero conditions, the couple, the principle of moments, center of gravity, and the worked application of a cyclist bending on a curve. The other branch develops moment of inertia, $I=\sum m_ir_i^2=MK^2$ (radius of gyration), computed by integration for a rod/ring/disc and extended to any axis via the parallel and perpendicular axis theorems, feeding into full rotational dynamics: $\tau=I\alpha$, work $=\tau\theta$, kinetic energy $=\frac12I\omega^2=L^2/2I$, power $=\tau\omega$, and the conservation of angular momentum ($L$ constant when $\tau=0$) whenever no external torque acts. …