An antique carousel that’s powered by a large electric motor undergoes constant angular acceleration from rest to full rotational speed in 5.00 seconds. when the ride ends, a brake causes it to decelerate steadily from full rotational speed to rest in 11.0 seconds. compare the torque that starts the carousel to the torque that stops it. τstart/τstop = the tolerance is +/-2%

1) For a rotating object, we can write the analogous of Newton's second law as

where  is the torque applied to the object, I is the moment of inertia and  is the angular acceleration.

2) We can write the ratio between the starting torque and the stopping torque as:


3) Then, we can rewrite the two angular accelerations. The general formula is

where  and  are the final and initial angular velocities, while t is the time. 

4) Let's start by calculating the starting acceleration. In this case, the initial velocity is zero, while the final velocity is the full rotational speed (let's call it , and the time is t=5.0 s:

When the carousel stops, instead, the initial velocity is  while the final velocity is 0, and the time is t=11.0 s:

Therefore, if we replace the two angular accelerations that we found into the formula of the torque ration written at step 2), we find:

where the negative sign simply means that the two torques have opposite direction. Therefore, the ratio between starting and stopping torque is 11:5.