# Torque in rotational motion

## Force and Torque

We know about the definition of force in linear motion as an external agent to change the state of rest or of uniform motion in a straight line according to Newton’s first law of motion. Similarly, the rotating force is required to change the state of rest or of uniform motion in a circular motion and that rotating force is called torque.

Torque is the moment of force. In other words, The rotating effect of force can be said as a torque. for e.g: applying force to open or close the door.

## Torque and expression of torque

Torque in rotational motion can be defined as the vector product of the perpendicular distance of a point of force from the axis of rotation and the force.

In Vector form:  where is the angle between and and is the unit vector along the direction of which gives the direction of .

The direction of Torque( ) is towards the perpendicular direction to both of and The magnitude of is: .

## Some Special Cases:

1) If then . So, 2) If then . So, So, we can define torque as the product of perpendicular force and distance from the axis of rotation.

## Couple and torque due to couple

If two equal forces act on a rigid body but in opposite directions such that the body undergoes rotational motion, these forces form a couple.

Since a couple forms a rotational motion, the moment of a couple (or Torque due to a couple) can be calculated by the product of either force with the perpendicular distance between them.

The torque due to couple = Force x perpendicular distance between them.

proof:

Suppose a wheel of radius is rotating about a center ‘O’ by the application of couple as shown in figure.

Torque at point A: Torque at point B: The total torque on a body is:    Hence, Torque due to force = Force x perpendicular distance between two forces.

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