Rotational work

Turning something takes energy in the same way pushing it does, and the bookkeeping has the same shape with rotational quantities swapped in.

EK 6.2.A.1 states the condition: a torque can transfer energy into or out of an object or rigid system if the torque is exerted over an angular displacement. No turning, no work, however large the torque. A hand holding a wrench still against a stuck bolt does none.

What each sheet prints. The AP Physics 1 and AP Physics 2 tables of information print $W = \tau\Delta\theta$. Both AP Physics C sheets print the integral form $W = \int \tau \cdot d\theta$ instead, which is what a torque that changes with angle needs.

Radians, or the number is wrong. $\tau$ is in newton metres and $\Delta\theta$ has to be in radians. Because the radian is a ratio of two lengths and carries no dimensions, the product comes out in joules with nothing left over. Substitute degrees and the answer is off by a factor of $180/\pi$ with no unit mismatch to warn you.

From a graph. EK 6.2.A.3: work done on a rigid system by a given torque can be found from the area under the curve of a graph of torque as a function of angular position. Same reading as force against displacement, one axis relabelled.

Sign works the same way too. A torque acting against the rotation, a bearing dragging on an axle, does negative work and removes energy.

Where the energy lands is rotational kinetic energy, and a rolling object splits it with the translational kind.