Rotational energy and angular momentum

The skill

A spinning object stores rotational kinetic energy, $K=\frac{1}{2}I{\omega }^2$, and carries angular momentum, $L=I\omega$. A torque acting through an angle does work, $W=\tau \mathrm{\Delta }\theta$; a torque acting for a time delivers an angular impulse $\tau \mathrm{\Delta }t$, which equals $\mathrm{\Delta }L$. With no net external torque, angular momentum stays constant, which is why a skater who pulls her arms in spins faster. The usual mistake is putting revolutions into $W=\tau \mathrm{\Delta }\theta$ instead of radians.