Torque (also known as moment, or moment of force) is the tendency of a force to cause or change the rotational motion of a body. It is a twist or turning force on an object. Torque is calculated by multiplying force and distance. It is a vector quantity, meaning it has both a direction and a magnitude. Either the angular velocity for the moment of inertia of an object is changing, or both.

## Units of Torque

The International System of Measurement units (SI units) used for torque is newton-meters or N*m. Even though newton-meters are equal to Joules, since torque isn't work or energy so all measurements should be expressed in newton-meters. Torque is represented by the Greek letter tau: *τ *in calculations. When it is called the moment of force, it is represented by *M*. In Imperial units, you may see pound-force-feet (lb⋅ft) which might be abbreviated as pound-foot, with the "force" implied.

## How Torque Works

The magnitude of torque depends on how much force is applied, the length of the lever arm that connects the axis to the point where the force is applied, and the angle between the force vector and the lever arm.

The distance is the moment arm, often denoted by r. It is a vector pointing from the axis of rotation to where the force acts. In order to produce more torque, you need to apply force further from the pivot point or apply more force. As Archimedes said, given a place to stand with a long enough lever, he could move the world. If you push on a door near the hinges, you need to use more force to open it than if you pushed on it at the doorknob two feet further from the hinges.

If the force vector *θ* = 0° or 180° the force will not cause any rotation on the axis. It would either be shoving away from the axis of rotation because it is in the same direction or shoving towards the axis of rotation. The value of torque for these two cases is zero.

The most effective force vectors to produce torque are *θ* = 90° or -90°, which are perpendicular to the position vector. It will do the most to increase the rotation.

## The Right-Hand Rule for Torque

A tricky part of working with torque is that it is calculated using a vector product. The torque is in the direction of the angular velocity which would be produced by it, so, the change in angular velocity is in the direction of the torque. Use your right hand and curl the fingers of your hand in the direction of rotation caused by the force and your thumb will point in the direction of the torque vector.

## Net Torque

In the real world, you often see more than one force acting on an object to cause torque. The net torque is the sum of the individual torques. In rotational equilibrium, there is no net torque on the object. There may be individual torques, but they add up to zero and cancel each other out.

## Sources and Further Reading

- Giancoli, Douglas C. "Physics: Principles with Applications," 7th ed. Boston: Pearson, 2016.
- Walker, Jearl, David Halliday, and Robert Resnick. "Fundamentals of Physics," 10th ed. London: John Wiley and Sons, 2014.