torque
/ tork /
Torque is the twist — the rotational cousin of force. A force pushes an object into motion; a torque turns it. You already know it in your hands: push a door near its hinges and it barely budges, but push at the far edge and it swings open easily. Same force, very different turning effect. That turning effect is torque, and it explains why doorknobs, wrenches, and see-saws are shaped and used the way they are.
Precisely, torque depends on the force and on where and in which direction you apply it: tau = r F sin theta, where r is the distance from the axis to where the force acts, F is the force, and theta is the angle between them. The combination r sin theta is the lever arm — the perpendicular distance from the axis to the line of the force — so we can also write tau = (lever arm) x F. The units are newton-metres (N m). A net torque is exactly what makes something start or stop spinning.
Like angular velocity, torque is really a vector, with a direction along the axis given by the right-hand rule (tau = r x F, a cross product). Push a wrench straight toward or away from the bolt (theta = 0) and you get zero torque no matter how hard you shove — only the sideways, perpendicular part of the push does any turning.
You push perpendicular to a door 0.8 m from its hinges with 20 N of force. The torque is tau = r F sin90 = 0.8 x 20 x 1 = 16 N m. Push at the same spot but only 30 degrees off the door, and you get 0.8 x 20 x sin30 = 8 N m.
Same force, same spot — but the angle changes the torque. Perpendicular pushes work best.
Torque has units of newton-metres, the same as the joule, but it is not energy — a torque is a twist, an energy is a capacity to do work; never add them.