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# The Physics of Carousels

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Since we're learning about rotational kinetmatics and such in class, I thought it would be a good idea to stick to circular motion.

So, carousels. Since we know that velocity equals distance over time, obviously the longer the distance the longer it would take to reach the destination. Carousel horses, though they may look like they're all moving at the same velocity, actually have different linear velocities depending on how far they are from the center of the carousel.

The more you think about it, the more it makes sense: horses on the outside have a longer distance to cover as the circumference of the outside of the carousel is bigger than any other inside horses' paths. So as the carousel spins, the horses on the outside have to maintain a faster linear velocity than the inside horses because they are covering more distance.

This concept, of course, we all learned or at least understood on some level from taking Physics B. Now that we're in Physics C, however, we can obseve the angular velocity. Whereas linear velocity is the change in distance over time, angular velocity is, as its name suggests, the change in the angle (theta) over time.

Though, in the carousel example, a horse close to the center has a slower linear velocity than a horse on the outside...each horses' angular change with respect to their starting positions is the same as the other horse! They'll both cover the same rotation in the same period of time. So we see, while linear velocity on a carousel depends on the horse's distance from the center, angular velocity remains constant for all horses.

bazinga818

## 1 Comment

How might you account for the up and down motion (and slight forward and backward motion with respect to the carousel floor) of the horses on the carousel?  As I seem to be spending quite a bit of time these days holding my two little ones on carousels, these thoughts keep popping into my mind pretty regularly.  Would be interesting to put a camera on a moving reference frame and see what sort of patterns you could develop.  Sine/cosine curves?

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