# Torque or Moment

Created | Updated Jun 27, 2006

*Torque* (as most people call it) or *moment* (as some engineers call it) is the rough concept of a 'turning force'. Since most people scratch their heads and look puzzled when it is referred to as a *moment*, it will hereafter be referred to as *torque*. When you turn a screwdriver or use a ratchet you are applying (if not necessarily caring about) the concept of torque.

Torque is a two- or three-dimensional^{1} physics construct used to explain the turning or twisting of objects.

### Newton

According to the venerable Sir Isaac Newton, any object for which forces balance will not experience acceleration and will stay in its current state of rest or motion. Objects at rest tend to stay at rest unless acted upon by an outside force; likewise, objects in motion tend to remain in motion unless acted upon by an outside force.

This is why wearing a seatbelt is generally a good idea and why towing with ropes or chains is generally a bad idea. But as this really isn't an entry about Newton at all, we'll get back to the real subject.

### Concept

For introductory Physics classes, for the sake of simplicity of calculation, forces are considered to apply evenly across the face of an object. For objects at a constant velocity (usually zero) a force (or sum of forces) pushes in one direction and a second force (or sum of forces) pushes back in the opposite direction. These forces cancel each other out nicely and you can happily go and do some number crunching.

Equal and opposite forces, however, are not the end of the story. Two equal and opposite forces applied to two distinct points on an object will not cause a straight line movement (translation) but they may cause a turning movement (rotation). If you don't believe this, try putting a small object on a flat surface and pushing the top in one direction and the bottom in the opposite direction.

This rotation force is called *torque* or *moment*.

### Applications

Probably the most common application of torque is the screwdriver and similar tools. You exert a net torque on the screwdriver and the screwdriver exerts a net torque on the screw (or your fingers if you're not careful).

Many tools that apply the concept of torque also apply levers to increase net torque. A handle running perpendicular to the axis of rotation will increase the torque applied without a need to increase the applied force. The longer the handle, the higher the ratio of torque to force.

Other applications of torque include small- and large-scale construction work, stress testing, many types of propulsion systems (e.g. electric motors, combustion engines etc.) and electric generators.

Some more everyday-type examples include the turning of a doorknob or using the ignition system of a car.

And let's not forget the humble spirograph^{2}.

### Mathematics of torque

The formula for torque is as follows:

T = F * d (F dot d)

Where:

- 'T' is torque (alternatively 'M' for moment)
- 'F' is the Force applied perpendicular to the axis of the object
- 'd' is the parallel distance between the force and the point for which you are calculating the moment (alternatively 'r' for radius)

To find the sum of moments, pick an arbitrary point to set as the 'point of rotation'. Calculate the moments as above. Set the moments that would cause the object to turn about its 'point of rotation' in one direction (usually anti-clockwise) to be positive. Set the moments that would cause the object to turn about its 'point of rotation' in the other direction to be negative. Add up all the moments to find the net moment acting on an object.

^{1}This is subject to verification since we have very little information pertaining to dimensions beyond the three we commonly refer to, including conclusive proof of their existence.

^{2}A toy which produces semi-unique, ink-inscribed patterns, based on the size, rotation, shape and pen position of various toothed pieces of plastic.