Question

If several forces act on a particle, the total torque on the particle may be obtained by first finding the resultant force and then taking torque of this resultant. Prove this. Is this result valid for the forces acting on different particles of a body in such a way that their lines of action intersect at a common point?

Answer 1

Explanation:

• Assuming n number of forces (f1, f2, f3, … fn) acting on a point H.
• Let O be a point at which moments of force (torque, (fi)) will be taken.
• So,
• f1 + f2 + f3 + … + fn = R __________ (1)
• fi at O will be
• τ1 = OH x f1
• Sum of torques at O will be
• M = OH x f1 + OH x f2 + … + OH x fn
• M = OH x (f1 + f2 + f3 + … + fn)
• Therefore, from (1) M = OH  x R  
• That is the torque of R (the resultant force) of the forces f1, f2, f3, … fn provides the sum of moments of torques.