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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 {\rm N} and Jerry pushes with a force of 35.5 {\rm N}, 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

τTom = 39.3 x 1.55 sin(60) = 52.75
τJerry = 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.
τTom =  +52.75
τJerry = -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 180^\circwithout 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

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