Luke and inga are riding the prince charming carousel at disney world. luke is on a horse 17 feet from the center. inga is on a horse 25 feet from the center. prince charming has the carousel spinning at 30 revolutions per minute. a. what is luke's angular speed (in radians/second)? rad/secb. what is inga's angular speed? (in radians/second)? rad/sec

We want to get Luke and Inga angular speed while they are on the carousel. Both of them have the same angular speed which is:

w = 3.14 rad/s

We define angular speed as the rotation speed of something that rotates, such that the angular speed is expressed in radians over time.

Here we do know that the carousel spins at 30 revolutions per minute, and each revolution has 6.28 radians, then the angular speed is given by:

w = (30*6.28 rad)/(1 minute)

But we want it on radians over seconds, then we can replace:

1 minute = 60 seconds to get:

w =  (30*6.28 rad)/(60 s) = 3.14 rads/sec

Notice that this angular speed will be the same for both Luke and Inga, because it only depends on the revolutions and not in the distance from the center.

If you want to learn more about angular speed, you can read:

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