# Rotational acceleration

1. Oct 10, 2015

### kolua

1. The problem statement, all variables and given/known data
Moving at its maximum safe speed, an amusement park carousel takes 12 s to complete a revolution. At the end of the ride, it slows down smoothly, taking 3.5rev to come to a stop. What is the magnitude of the rotational acceleration of the carousel while it is slowing down?

2. Relevant equations
w2=wo2+2alpha theta

3. The attempt at a solution
plug in and get -pi/144 rad/s2 is this right???

2. Oct 10, 2015

### kolua

or -pi2/504 s-2

3. Oct 10, 2015

### Daeho Ro

When it moves with maximum speed, the angular velocity is $\omega_i = \pi / 12.$ You want to stop it within $3.5$ revolution, that is $\theta_f - \theta_i = 7\pi$ and it have to be $\omega_f = 0.$ Then, you can get the angular acceleration, $\alpha.$

4. Oct 10, 2015

### kolua

shouldn't the angular velocity be pi/6?

5. Oct 10, 2015

### Daeho Ro

Oh, yes I missed the factor $2$.

6. Oct 10, 2015

### kolua

Can you also help me check this one? You hold a small ice cube near the top edge of a hemispherical bowl of radius 100 mm. You release the cube from rest. What is the magnitude of its acceleration at the instant it reaches the bottom of the bowl? Ignore friction. is a=2g=19.6 m/s2

7. Oct 10, 2015

### ehild

Which one?

Always show your work in detail.