Torque

Consider pushing on a door to open it. If you push near the hinges, it’ll take a very large applied force to make the door open. However, if you push far away from the hinges, a much smaller force is necessary. The reason is that the door is not made to rotate by merely the application of a force; rather, the applied torque has the necessary effect. Torque is symbolized by the lowercase Greek letter tau and can be expressed by or .

As we can see from the first of the two equations above, torque is dependent on both the force applied and the radius at which it is applied. In the case of the door, the radius in question is the distance from the hinges (the axis of rotation) at which the force is applied. Torque is measured in units of , which are dimensionally equivalent to but should never be stated as such, since they are conceptually different.

Note also the cross product in the first expression of torque. The cross product takes into account the perpendicular component of the applied force. Therefore if you push on the door at an angle, it will be less effective than if you exert the force head-on. Also, remember to use the right hand rule in determining the torque’s direction.

Torque frequently crops up in questions, particularly on the multiple choice section of the AP exam, in terms of balancing torques such that rotation does not occur. In these situations, it’s simply necessary to treat the problem similarly to a situation involving the balancing of forces. Torque is also often important in considering more “advanced” versions of force problems in which pulleys have rotational inertia.