Torque and Couple

Suppose O is a fixed point in the body and it can rotate about an axis passing through this point. Let a force of magnitude F be applied at the point A along the line AB.

If AB passes through the point O, the force F will not be able to rotate the body. The farther is the line AB from O, the greater is the ability of the force to turn the body about the axis through O. The turning effect of a force is called torque. Its magnitude is given by

τ = Fs = Fr sin θ

where s is the distance between the axis of rotation and the line along which the force is applied.

The units of torque are newton-metre, or Nm. The torque is a vector quantity.

τ = r × F

which gives both magnitude and direction of the torque. τ is perpendicular to the plane containing vectors r and F. If you extend the thumb of the right hand at right angles to the fingers and curl the fingers so as to point from r to F through the smaller angle, the direction in which thumb points is the direction of τ.

If there are several torques acting on a body, the net torque is the vector sum of all the torques.

Couple

Two equal and opposite forces having different lines of action are said to form a couple whose torque is equal to the product of one of the forces and the perpendicular distance between them.