The body in shown figure is pivoted at $O$ , and two forces act on it as shown,
(a) Find an expression for the net torque on the body about the pivot.
(b) If $r_{1} = 1.30 m, r_{2} = 2.15 m, F_{1} = 4.20 N, F_{2} = 4.90 N, θ_{1} = 75^{\circ}$ and $θ_{2} = 60^{\circ}$ , what is the net torque about the pivot?

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Solution

(a) Take a torque that tends to cause a counter clockwise rotation to be positive and a torque that tender to cause a clockwise rotation to be negative. Thus a positive torque of magnitude $r_{1} F_{1} sin θ_{1}$ is associates with $_{1}$ and a negative torque of magnitude $r_{2} F_{2} sin θ_{2}$ is associated with $_{2}$ . Both of these are about $O$ . The net torque about $O$ is $τ = r_{1} F_{1} sin θ_{1} - r_{2} F_{2} sin θ_{2}$ .
(b) Substitute the given values of obtain $τ = (1.30 m) (4.20 N) sin 75^{\circ} - (2.15 m) (4.90 N) sin 60^{\circ} = - 3.85 N - m$ .

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The body in shown figure is pivoted at O, and two forces act on it as shown,(a) Find an expression for the net torque on the body about the pivot.(b) If r1=1.30 m,r2=2.15 m,F1=4.20 N,F2=4.90 N,θ1=75∘ and θ2=60∘, what is the net torque about the pivot?