Torque and Work
A torque that turns a body through an angle does work on it. For a constant torque, $W_{rot} = \tau\,\Delta\theta$. When $\tau$ varies, $W_{rot}$ is the signed area under the $\tau$-vs-$\theta$ graph. That work is what changes the body's rotational kinetic energy: $W_{net,\,rot} = \Delta K_{rot}$.
Two pieces follow. Doubling $\Delta\theta$ at the same torque doubles the work. A torque pointing opposite to the rotation does negative work; it takes $K_{rot}$ out instead of putting it in.
Three traps come up. Reading the area under any $\tau$-graph as work (only $\tau$-vs-$\theta$ gives work; $\tau$-vs-$t$ gives angular impulse). Treating negative work as a smaller amount, or as no work at all. Attaching a direction to $W$, which has none.
The work
3 ways in · any order
Lesson
Torque and Work
›
Five sections. The formula $W_{rot} = \tau\,\Delta\theta$, signed area as work, the rotational work-energy theorem, three named pitfalls, and a ten-scenario skill check.
Diagnostic
10-item topic check
›
Ten items: reading area under $\tau$-vs-$\theta$, handling negative work, telling $\tau\Delta\theta$ from $\tau\Delta t$, and chaining $W_{rot} = \Delta K_{rot}$.
Targeted Practice
Drill a single misconception
›
Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the misconception and you move on.