Question

A merry-go-round accelerates from rest to 0.75 rad/s in 33 s.

Assuming the merry-go-round is a uniform disk of radius 6.0 m and mass 3.20×104 kg , calculate the net torque required to accelerate it.

Answer 1

1309.1 Nm

Step-by-step explanation:

Torque is given as a product of Moment of innertia and acceleration hence

T=Ia where T is torque and a is acceleration

To get acceleration, it is rate of change of speed per unit time hence
`a=\frac {v_f-v_i}{t}` where v and t represent velocity and time respectively while subscripts f and i represent final and initial respectively. Also, I is given by
`0.5mr^(2)` where m js mass and r is radius hence the net torque can now be written as

`T=0.5mr^(2)* \frac {v_f-v_i}{t}`

By substituting the given figures then

`T=0.5* 3.2* 10^(4)* 6^(2)* \frac {0.75-0}{33}=1309.0909090867 Nm\approx 1309.1 Nm`