The body in the figure

Question

The body in the figure is pivoted at O, and two forces act on it as shown. If r1=2.87 m, r2=3.61 m, F1 = 3.26 N, F2 =4.87 N Theta 1 = 60.0 degrees and Theta 2 = 54.0 degrees.

what is the net torque about the pivot ?

Answer 1

The equation for torque is

τ = F r sinθ

F is the force, r is the distance from the axis of rotation and where the force is applied, and θ is the angle between r and F. The angle between F and r can be confusing so make sure to place the tail of both vectors at a common origin. The angle starts at r and goes to F. If the angle is counter-clock wise it is positive. If the angle is clock-wise the angle is negative. A diagram comes with this problem and from that diagram θ₁ is positive and θ₂ is negative.

The sum of torques then gives,

τ = (3.26 N)(2.87 m) sin(60) + (4.87 N)(3.61 m) sin(-54)

τ = -6.12 Nm