AP Physics 1 · Summary

Unit 6 summary

1. Rotational kinetic energy is $\frac{1}{2}I\omega^2$; a constant torque does work $\tau\Delta\theta$, and net work equals the change in rotational kinetic energy.
2. Angular momentum is $I\omega$, or $mvr_\perp$ for a point mass; a torque changes it by $\tau\Delta t$.
3. With no net external torque, $I_i\omega_i = I_f\omega_f$, but rotational kinetic energy can still change.
4. Rolling without slipping: $v = \omega R$, total K is translational plus rotational, and the static friction at the contact point does no work.
5. From rest, $v = \sqrt{2gh/(1 + \beta)}$ for $I = \beta MR^2$: shape decides the race, not mass or radius.
6. Circular orbit: $v = \sqrt{GM/r}$ and $T^2 = 4\pi^2r^3/(GM)$. In any orbit, angular momentum and total energy stay constant, so the object is fastest when closest; escape needs $\sqrt{2GM/R}$.