Answer:
τ = 1679.68Nm
Step-by-step explanation:
In order to calculate the required torque you first take into account the following formula:
(1)
τ: torque
I: moment of inertia of the merry-go-round
α: angular acceleration
Next, you use the following formulas for the calculation of the angular acceleration and the moment of inertia:
(2)
(3) (it is considered that the merry-go-round is a disk)
w: final angular speed = 3.1 rad/s
wo: initial angular speed = 0 rad/s
M: mass of the merry-go-round = 432 kg
R: radius of the merry-go-round = 2.3m
You solve the equation (2) for α. Furthermore you calculate the moment of inertia:

Finally, you replace the values of the moment of inertia and angular acceleration in the equation (1):

The required torque is 1679.68Nm