Question
Show that torque produced by force on the body is equal to product of the force and perpendicular distance of line of action of force from the axis of rotation or it is equal to the product of radial distance of point of action of force from the axis of rotation and transverse component of force.
Solution
Consider a particle moving along the curve PQ under the influence of a force 
.
Let at any instant r, the particle be at A and its position vector is 
. 
Torque is given by, 
where,
Fϕ is transverse component of force.
Therefore, torque is equal to the product of radial distance and transverse component of force.
Also,
x = τ Fsin ϕ
= F(rsin ϕ)
= Fd
Therefore, torque is equal to the product of the magnitude of force and perpendicular distance of line of action of force from the axis of rotation.
