Question

An antique carousel that's powered by a large electric motor undergoes constant angular acceleration from rest to full rotational speed in 6 seconds. when the ride ends, a brake causes it to accelerate steadily from full rotational speed to rest in 9.2 seconds. compare the torque that starts the carousel to the torque that stops it.

Answer 1

during the acceleration the time taken to reach full speed is 6 s

so angular acceleration will be given as

`\alpha = (\omega)/(6)`

now from the same maximum speed it will stop in time t = 9.2 s

so deceleration is given as

`\alpha' = (\omega)/(9.2)`

now we can say initially the torque will be given as

`\tau_1 = I *(\omega)/(6)`

`\tau_2 = I*(\omega)/(9.2)`

now we have

`(\tau_1)/(\tau_2) = 9.2/6 = 1.533`