Torque

Torque is the rotational analog of force.

Force causes linear acceleration; torque causes angular acceleration.

In order to lift a stone by using a lever, a force is required (see figure 10.12). The effectiveness of the force depends both on its direction and where it is applied relative to the pivot point.

The turning ability of a force about an axis or pivot is called its torque.

The torque of a force F that acts at a distance r from the origin is defined as

 T = rF sinθ (10.20)

Where θ is the angle between the vector r and F, as shown in the figure (10.13).

The definition of torque (equation 10.20) may be interpreted in two ways:

(i) T = r (Fsinθ) = r  ⊥ F

The turning effect of a force about the origin is produced only by the perpendicular component (F⊥ = F sin θ) as shown in the figure (10.8 b).

(ii) T = (r sinθ) F = r_⊥ F

Where r⊥ is the perpendicular distance from the origin to the line of action of the force as shown in the figure (10.8 a). It is also called the lever arm.