# What is Torque? Definition, Formula and more

##### Abstract

The effect of a force that made the object rotate or turn about its axis is called torque. The rigid body made up of small particles and is not deformed on applying force when rotate about a line, all particles with their centers push this line and this is called the axis of rotation.

The line along which turning effect is acting is called the line of action of force. The perpendicular distance between axis of rotation and the line of action is the moment arm. Mathematically, torque is a product of force F and moment arm L. Torque = F x L. Torque depends on moment arm. The longer the moment arm greater the torque will produce.

##### Torque Definition

“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.

###### Rigid Body

A body is made up of a large number of small particles. If the distances between all sets of particles of the body do not change by using 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 upon it.

###### Axis of Rotation

Think about a rigid body rotating about a line. The particles of the body move in circles with their centres all pushing this line. This line is called the axis of rotation of the body.

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

##### Explanation of Torque

Let us study the factors on which torque or moment of a force depends. You may have seen that a mechanic uses a spanner to loosen or tighten a nut or a bolt. A spanner having long arm helps him to do it with higher ease than the one having a short arm.

It is due to the fact that the turning effect of the force is different in the two cases. The moment produced by a force using a spanner of the longer arm is greater than the torque produced by the exact same force but using a spanner of the much shorter arm.

##### Line of Action of a Force

The line along which a force act is called the line of action of the force.

###### 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.

##### Mathematical Expression

The torque or moment of a force depends upon the force F and the moment arm L of the force. Greater is a force, higher is the moment of the force. Similarly, longer is the moment arm higher is the moment of the force. Therefore, the moment of the force or torque τis figured out by the product of force F and its moment arm L. Mathematically,

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We now consider the torque due to a force F acting on a rigid body. Let the force F acts upon a rigid body at the point- P whose position vector relative to pivot O is r. The force F can be resolved into two rectangle-shaped components, F sin θ perpendicular to r and F cosθ along the direction of r. The torque due to F cosθ about pivot O is zero as its line of action travels through point O. For that reason, the magnitude of torque due to F is, equal to the torque due to F in just about O. It is provided by

Alternatively, the minute arm l is equal to the magnitude of the element of r perpendicular to the line of action of F.Thus,

τ=r x f

where θ is the angle in between r, and F.

it can be seen that the torque can be specified by the vector of position vector r and the force F, so

τ=r Fsinθ

Just as force figures out the linear velocity produced in a body, the torque acting on a body identifies angular acceleration. Torque is the comparable of force for rotational motion. If the body is at rest or turning with uniform angular speed, the angular acceleration will be absolutely zero. In this case, the torque acting upon the body will be absolutely zero.

###### SI Unit

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