Mechanics

# Torque:definition,formula,unit and examples

## Definition of torque in physics

“The turning effect of a force is called torque or moment of the force.”

We open or close a door by pushing or pulling it.Here push or pull turn the door about its hinge or axis of rotation.The door is opened or closed due to the turning effect of the force acting on it.

Before we go to learn about we will learn few terms related with torque.

## Rigid body

A body is composed of large number of small particles of the body do not change by applying a force then it is called a rigid body.In other words ,a rigid body is the one that is not deformed by force or forces acting on it.

## Axis of rotation

The line along which body rotates is called axis of rotation. Consider a rigid body rotating about a line.The particles of the body move in circles with their centres  all lying on this line.This line is called the axis of rotation of the body.

Forces that produce turning effect are very common. Turning pencil in a sharpener, turning stopcock of a water tap, turning doorknob and so on are some of the example where a force produces turning effect.

“The turning effect of a force is called torque or moment of the force.”

We can open or close a door more easily by applying a force at the outer edge of a door rather than near the hinge.Thus,the location where the force is applied to turn a body is very important.

Let us study the factors on which torque or moment of a force depends. You might have seen that a mechanics uses a spanner as shown in figure to loosen or tighten a nut or a bolt. A spanner having long are helps him to do it with greater ease than the one having short arm. It is because the turning effect of the force is different in the two cases.The moment produced by a force using a spanner of longer arm is greater than the torque produced by the same force but using a spanner of shorter arm.

## Line of Action Of a Force

The line along which a force acts is called the line of the action of the force, line BC is the line of action of a force F.

## Moment Arm

The perpendicular distance between the axis of rotation and the line of action of the force is called the moment arm of the force. It is represented by the distance L. The torque or moment of a force depends upon the force F and the moment arm L of the force.Greater is a force, greater is the moment of the force.Similarly,longer is the moment arm greater is the moment of the force. Thus the moment of the force or torque (        τ        ) is determined  by the product of force F and its moment arm L.

## Equation for torque

τ = F×L

## What is the unit of torque in physics?

SI units of torque is newton-meter (Nm). A torque of 1 N  m is caused by a force of 1 N acting perpendicular to the moment arm 1 m long.

## Principle of Moments

“A body balanced if the sum of clockwise moments acting on the body is equal to the sum of anticlockwise moments acting on it.”

A force that turns a spanner in the clockwise direction is generally used to tighten a nut.The torque or moment of the force so produced is called clockwise moment.On the other hand,to loosen a nut, the force is applied such that it turns the nut in the anticlockwise direction.The torque or moment of the force so produced is called Anticlockwise moment.

A body initially at rest does not rotate if sum of all the clockwise moments acting on it is balanced by the sum of all the anticlockwise moments acting on it. This known as the principle of moments.According to the principle of moments.

## Couple moment

“A couple is formed by two unlike parallel forces of same magnitude but not along the same line.”

When a driver turns a vehicle, he applies forces that produce a torque. This torque turns the steering wheel. These forces act on opposite sides of the steering wheel, and are equal in magnitude but opposite in direction. These two forces from a couple.

A double arm spanner is used to open a nut. Equal forces each of magnitude are applied on ends A and B of a Spanner in opposite direction. These forces form a couple that turns the spanner about point O. The torque produced by both the force of a couple have the same direction. Thus, the total torque produced by the couple will be

Total torque of the couple=F×OA +F×OB

=F(OA + OB)

Therefore:

Torque of the couple = F × AB

In this equation gives the torque produced by a couple of forces F and F  separated by distance AB. The torque of a couple is given by the product of one of the two forces and the perpendicular distance between them.

Watch also video:

External sources

• https://en.wikipedia.org/wiki/Torque
• https://www.physics.uoguelph.ca/tutorials/torque/Q.torque.intro.html