Angular Momentum (Physics)

Recall cards on angular momentum and rolling motion. Rolling without slipping: the contact point is instantaneously at rest, v_CM = R omega, a_CM = R alpha, and d_CM = R theta; the acceleration down an incline a_CM = m g sin(theta)/(m + I_CM/r^2), the static-friction bound needed to prevent slipping, and the split of kinetic energy into translational (1/2) m v_CM^2 plus rotational (1/2) I_CM omega^2 with friction doing no work. Angular momentum of a particle: l = r x p, magnitude r p sin(theta), direction by the right-hand rule, the lever-arm form l = r_perp m v, and the unit kg m^2/s. The rotational form of Newton's second law, sum tau = dl/dt, and for a system sum tau_ext = dL/dt. Angular momentum of a rigid body, L = I omega, directed along the rotation axis. Conservation of angular momentum when the net external torque is zero: I omega = I' omega', the ice-skater effect, and the rise in rotational kinetic energy K'_rot = K_rot (I/I'). And the precession of a gyroscope: gravitational torque tau = r M g sin(theta) perpendicular to L, the precession rate omega_p = r M g/(I omega), nutation, and Earth's 26,000-year precession.