Net Torque and Sign Conventions

Torque measures how hard something twists, and like force, it has a direction baked into it. Instead of left-right or up-down, torque direction is rotational: clockwise or counterclockwise around a chosen pivot. The fix is the same trick you used for force vectors: pick one direction as positive. Counterclockwise positive is the common choice. Once you commit, every torque becomes a signed number, and finding net torque is just adding them up. Two torques twisting opposite ways partly or fully cancel, same as two forces pulling opposite ways on a rope.

This is why two people pushing a merry-go-round from opposite sides can cancel: if their torques are equal in size but opposite in rotational direction, the signed sum is zero, even though both are clearly pushing hard. Nothing mysterious is happening physically — the rod or wheel just has no tendency to spin either way.

The catch is that torque is always torque about some axis, and the lever arm distance depends on where you put that axis. If the net force on an object isn't zero, moving the pivot changes each force's lever arm by a different amount, so the net torque you calculate can come out different for different axis choices. Only when the net force is zero does net torque become the same no matter where you put the axis — a fact that becomes essential once you reach equilibrium problems, where you get to choose the pivot for convenience.