Calculate the net torque about the axle of the wheel shown i

Calculate the net torque about the axle of the wheel shown in the figure (Figure 1) . Assume that a friction torque of 0.40 mN opposes the motion. Express your answer using two significant figures.

Solution

According to the given problem,

As we simply going to add the torques,

Assuming clock wise torques[CW] are +ve, and anti clockwise[ACW] torques -ve.

All angels are 90^o so it makes it pretty easy: Then 135^o angle is not relevant

t₃₅ = rF = 0.12 m*35 N = +4.2 Nm CW
t₂₈ = -rF = -0.24 m*28 N = -6.72 Nm ACW
t₁₈ = rF = 0.24 m*18 N = +4.32 Nm CW

Adding all these together:
t = +1.92 Nm CW

As there is a 0..4 Nm torque is opposing the motion, lets assuming that the object is rotating CW, then the .40 Nm torque would be acting ACW, and the net torque would be:

t = +1.5 Nm - 0.40 Nm = 1.5 Nm CW