Torque
A force pushes. A torque turns. How much a force rotates an object depends on three things: the size of the force, the distance from the axis to where it's applied, and the angle between them. Drop any one to zero and the torque is zero, no matter how hard you push. The headline equation, $\tau = rF\sin\theta$, says this in symbols; the lab below says it in motion.
Three traps in this topic. The first treats torque as just force, ignoring the lever arm: bigger push, bigger torque, no matter where it lands. The second drops the angle from the formula whenever the force is not perpendicular to the radius vector, using $rF$ where $rF\sin\theta$ is needed. The third reports a torque without naming the axis. The same force gives different torques about different axes; about any axis on the force's line of action, the torque is zero. The lesson walks through each one with a worked example.
The work
3 ways in · any order
Lesson
Torque
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Frame torque as the rotational version of force, build the formula $\tau = rF\sin\theta$, work two examples (one perpendicular, one at an angle), and set the CCW-positive sign convention. Closes with a ten-scenario applet drilling the three places torque problems tend to break: forgetting the lever arm, dropping the angle, and computing a torque without naming the axis.
Diagnostic
10-item topic check
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Ten items: three symbolic, three factor-of-change, three quantitative, one synthesis. Wrong-answer chips are tagged so the player can route you to the right targeted drill when you miss. Roughly 12 to 15 minutes; your work is saved.
Targeted Practice
Drill a single misconception
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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.