# Torque is a Rotational Force

by Ron Kurtus (revised 31 October 2015)

A * torque* is a special form of force that turns an axle in a given direction. It is sometimes called a

*.*

**rotational force**You can create a torque by pushing on a rod or lever that rotates an axle. Likewise, a torque on an axle can result in a linear force at a distance from the center of the axle.

Questions you may have include:

- What are the relationships in a torque?
- How can you create a torque?
- How is a torque used to create a linear force?

This lesson will answer those questions. Useful tool: Units Conversion

## Relationship of torque and force

A force is defined as a push in a specific direction that moves an object. It is considered linear or moving in a straight line. On the other hand, a torque is a force that rotates an axle or wheel around its center.

The relationship between torque and force is:

T = FRor

F = T/R

where

**T**is the torque in foot-pounds or newton-meters**F**is the force in pounds or newtons**R**is the radius or distance from the center to the edge in feet or meters**FR**is**F**times**R****T/R**is**T**divided by**R**

**R** is also sometimes called the *moment arm*. The force, **F**, is applied perpendicular to the radius, lever or moment arm.

## Creating a torque

A requirement for creating a torque is that the object must be able to rotate about some center point. Some examples are a wheel that can rotate on an axle, a bolt that is constrained to turn in a hole, and the axle of a lever or teeter-totter.

By applying a force on the edge of a wheel, you create a torque that rotates the wheel. Likewise, by applying a force on a wrench, you can rotate a bolt within its hole.

Force on wrench creates torque on bolt

If the force on the wrench is 10 pounds and the length of the wrench is 6 inches, the torque created is 10 pounds times 0.5 foot = 5 foot-pounds.

If the force on the wrench is 0.5 newtons and the length of the wrench is 20 centimeters, the torque created is 0.5 newtons times 0.2 meters = 0.1 newton-meters.

## Creating force from torque

A torque on the axle of a wheel can be transferred into a force on the circumference of the wheel.

Torque applied to wheel results in force on edge

You can demonstrate this force by placing a bicycle up-side-down and spinning one of its wheels. Touching the outer surface of the wheel, you can feel the force pushing your hand in the direction of rotation. (Obviously, don't be so foolish to stick your fingers in the spokes of the spinning wheel.)

## Summary

A torque is a special form of force that turns an axle in a given direction. Torque equals force times moment arm. Pushing on a rod that rotates an axle can create a torque on that axle. Likewise, a torque on an axle can result in a linear force at a radius from the center.

Keep a positive attitude

## Resources and references

### Websites

### Books

**The Science of Forces** by Steve Parker; Heinemann (2005) $29.29 - Projects with experiments with forces and machines

**Glencoe Science: Motion, Forces, and Energy**, by McGraw-Hill; Glencoe/McGraw-Hill (2001) $19.32 - Student edition (Hardcover)

**Top-rated books on Physics of Force**

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## Torque is a Rotational Force