Torque or Moment of Force

A force can rotate a nut when applied by a wrench or it can open a door while the door rotates in its hinges (i.e.) in addition to the tendency to move a body in the direction of the application of a force, a force also tends to ratate the body about any axis which does not intersect the line of action of the force and also not parallel to it. This tendency of rotation is called turning effect f a force or moment of the force the given axis. The magnitude of the moment of force F about a point is defined as the product of the magnitude of force and the perpendicular distance of the point from the line of action of the force.

If the particle rotating in xy plane about the origin under the effect of force and at any instant the position vector of the particle is

then,

                                           Torque

 

τ = r F sinφ

[where φ is the angle between the direction of and ]

1. Torque is an axial vector. i.e., its direction is always perpendicular to the plane containing vector and in accordance with right hand screw rule. For a given figure the sense of rotation is anti-clockwise so the direction of torque is perpendicular to the plane, outward through the axis of rotation.
2. As          τ = r F sinφ

Or          τ = F (r sinφ) = Fd       [As d = r sinφ from the figure]

i.e. Torque = Force ´ Perpendicular distance of line of action of force from the axis of rotation.

Torque is also called as moment of force and d is called moment or lever arm.