establish the relation between torque and force

NEET Class neet Answered

establish the relation between torque and force

Asked by anshikabhardwaj272003 | 23 Jan, 2022, 16:56: PM

Expert Answer

If a force acts on a single particle at a point P whose position with respect to the origin O is

given by the position vector

begin mathsize 14px style r with rightwards arrow on top end style

as shown in figure , then the moment of the force or Torque

acting on the particle with respect to the origin O is defined as the vector product

begin mathsize 14px style tau with rightwards arrow on top space equals space r with rightwards arrow on top cross times F with rightwards arrow on top end style

The torque is a vector quantity. The magnitude of τ is

τ = rF sinθ

where r is the magnitude of the position vector r, i.e. the length OP, F is the magnitude of force
and θ is the angle between r and F as shown in figure.

The SI unit of moment of force is Newton-metre (Nm).

The magnitude of the torque is written as

τ = (r sinθ )F = r_⊥F

τ = rF sinθ = rF_⊥ (7.24c)

where r_⊥ = r sinθ is the perpendicular distance of the line of action of F form the origin and
F_⊥ = F sinθ is the component of F in the direction perpendicular to r.

Torque τ = 0 if r = 0, F = 0 or θ = 0^o or 180^o . Thus, the torque vanishes if either the magnitude of
the force is zero, or if the line of action of the force passes through the origin.

Answered by Thiyagarajan K | 23 Jan, 2022, 17:36: PM