The body in figure shown is pivoted at O and two forces acts on it as shown

(i) Find an expression of the net torque on the body about the pivot
(ii) If `r_(1)=1.30 m,r_(2)=2.15 m,F_(1)=4.20N,F_(2)=4.90 N,theta_(1)=75^(@)` and `theta_(2) = 60^(@)`, what is the net torque about the pivot ?

Explanation

(i) Take a torque that tends to cause a counter clockwise rotation from rest to be positive and a torque that tends to cause a closkwise rotation from rest to be negative. Thus, a positive torque of magnitude `r_(1)F_(1) sin theta_(1)` is associated with `F_(1)` and negative torque of magnitude `r_(2)F_(2) sin theta_(2)` is associated with `F_(2)`. Both of these are about O. The net torque about O is `tau = r_(1)F_(1) sin theta_(1)=r_(2)F_(2) sin theta_(2)`
(ii) Substitute the given values to obtain
`tau=(1.30m)(4.20N)sin 75^(@)-(2.15m)(4.90N)sin 60^(@)=-2.85 Nm`.