Torque

Torque measures how strongly a force twists a body about an axis. In Physics C it is a vector, the cross product τ = r × F of the position vector r, from the axis to where the force acts, and the force F. Its size is τ = rF sinθ, set by the part of the force perpendicular to r, and its direction follows the right-hand rule, out of or into the page along ±k. That same size has a second reading: F times the lever arm r sinθ, the perpendicular distance from the axis to the force's line of action.

Torque rarely fails in the numbers; it fails in the setup. Dropping the sinθ factor and using the bare product rF, right only when the force is perpendicular. Getting the direction wrong from the cross product — placing the torque in the plane of r and F, or reversing r × F into F × r. And using the full distance to where the force acts instead of the perpendicular lever arm r sinθ. Fix those three and torque becomes routine.