What is the Torque?

Tom and Jerry both push on the 3.10 m-diameter merry-go-round shown in the figure.

If Tom pushes with a force of 39.3  and Jerry pushes with a force of 35.5 , what is the net torque on the merry-go-round?

Known variables:

diameter: 3.10 m or

radius: 1.55 m

Force_1= 39.3 N

Force_2: 35.5 N

Force_1 angle: 60°

Force_2 angle: 80°

First off, we would need to find torque of each person

the equation of torque is as follows: τ = Frsinθ

τ_Tom = 39.3 x 1.55 sin(60) = 52.75
τ_Jerry = 35.5 x 1.55 sin(80) = 54.19

Since we know that the direction of the rotation is clockwise, we can determine the signs for the torque.
τ_Tom =  +52.75
τ_Jerry = -54.19

Just add the torques together to find the net torque.

τ= τ1 + τ2

τ= 52.75 + -54.19

τ= -1.44 N*m

2) What is the net torque if Jerry reverses the direction that he pushes by 180without changing the magnitude of his force?

If Jerry reverses the direction, then we would just have to add the torques.

τ= 52.75 + 54.19

τ=107 N*m