Torque

Torque (Rotational dynamics)

Torque(τ)

Torque is the turning effect of a force on a body, on which the force acts.

The turning effect of a force depends on 

(i) the magnitude of the force and 

(ii) the perpendicular distance from the axis of rotation to the line of action of the force

Definition

The moment of the applied force is called torque. It is represented by the symbol ‘τ’.

If F is the force acting on a body at a distance r (Fig. 1.40) then,

Torque = Force × distance

i.e., τ = F × r

The rotational motion comes into picture only when the torque acts on the body. 

Torque in vector notation

When a force is applied on a rigid body capable of rotation about some axis, the body rotates about the axis.

The ability of a force to rotate a body about an axis is measured in terms of a quantity called torque.

Consider a body capable of rotation about an axis passing through O. Let a force F act at A, distance 'r’ from O such that the line of action of the force is perpendicular to OA.

The moment of this force F about the axis through O is a measure of the torque. (Fig 1.40)

If the direction of the force is inclined at an angle θ with the direction of r, it is measured as the product of the force F and the perpendicular distance from the axis of rotation to the line of action of the force.

∴ Torque = F × ON = F × d = F.r sin θ

This can be expressed in vector form as

Thus torque is the cross product of force and the vector between the axis of rotation and the point of application of the force.

It is acting in a direction perpendicular to the plane containing and its direction is given by right hand screw rule.

If perpendicular to each other τ = rF

(⸪ θ = 90° and sin θ = 1)