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NEET Class neet Answered

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 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 = 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.
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