Question

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

Answer 1

Answer:

1309.1 Nm

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

$T=0.5mr^{2}\times \frac {v_f-v_i}{t}$

By substituting the given figures then

$T=0.5\times 3.2\times 10^{4}\times 6^{2}\times \frac {0.75-0}{33}=1309.0909090867 Nm\approx 1309.1 Nm$