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establish the relation between torque and force
Asked by anshikabhardwaj272003 | 23 Jan, 2022, 04:56: 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 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 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 = rF

or
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 = 0o or 180o . 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, 05:36: PM
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