Ok, If I stand on a (rotating) carousel and a friend stands opposing me…can I throw him a ball straight across? Let’s forget the Coriolus effect, for now. And, assume no
obstacles - such as those objects found on a carousel!
If the answer is yes, then could there be some speed at which the carousel rotates so that I could throw the ball AND then catch it myself - once rotated 180 degrees?
These things bug me late at night…
Isn’t that the same as saying the carousel ISN’T rotating? I’m not understanding why you want to remove that influence, since it appears (to me, at least) to be the one thing complicating the question.
But if you ignore the Coriolis effect (“assume, for the sake of simplicity, that the cow is spherical…”), sure you can throw a ball to your friend, the same way you could throw a ball to him if you both stepped off the carousel and stood on a patch of grass 20 feet away.
The speed at which the carousel would need to rotate for you to be able to throw and catch the ball depends on how hard you throw the ball and the diameter of the carousel. The carousel needs to turn 1/2 revolution in the time it takes for the ball to travel the diameter of the carousel. Calling the diameter (measured in feet) d, and the time (in seconds) of the ball’s travel time t, the carousel revolves once every 2t seconds, and a point on the edge of the carousel travels pi * d feet (the circumference of the carousel) in that time. So, the ratio of seconds to circumferential travel is 2t : (pi * d). Multiply by 30, and you get 60t : 30(pi * d), which means 30(pi*d) RPM. As with any ratio, if you vary one side, say by throwing the ball harder, you’ll have to change the value of the variable on the other side to keep the ratio proportional, in this case by increasing the diameter.
I’ll take a shot at it, because I think the answer is pretty simple. I may be forgetting some complication, though, so someone can correct me.
Say that the stationary ground is numbered like a clock, and the thing is rotating clockwise. So you’d pass by the 12, then the 1, the 2, and so on. If you’re at the 12 and your friend is at the 6, throwing the ball like you would on the ground toward your friend will not only miss him, but miss the 6. Instead, the ball will veer off toward the 4 or 5. You could, however, throw the ball toward what you thought was the 7, and have it hit the 6. I don’t know if this is the Coriolis force in action, but I don’t think you can ignore it if it is. The angular speed [Sym]w[/Sym] is very large in comparison with Earth’s (I’m assuming). If you wanted your friend to catch the ball, you should try to throw it toward the 9. Then, it would veer off toward the 7, which is where your friend is by the time it gets around to him. As to whether you could throw it to yourself, yes, but, as I think typo mna is saying, that would have to be one very fast carousel.
You can throw a ball to a friend on a carousel, but you cannot throw it “straight across.”
While you hold the ball, it has the same velocity you do (assume the carousel is rotating counterclockwise and we view from above). When you throw it “straight,” I assume you mean applying a force directed along the diameter between you and your friend (and not trying to lead your friend with the throw). Once you apply this force and let the ball go, it’s velocity (speed and direction) is a composite of the force you apply along the diameter and the original velocity of the ball along the direction of rotation. Let me see if I can draw it.
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Nope, guess I can’t. Anyway, rather than go straight across, the ball will go diagonally to the right (from a fixed perspective at the point of release
Seven friends and I once tried playing catch on a playground carousel. (It had 8 metal “horses” that we could each sit on.)
We got it spinning slowly and started playing. I found that by throwing it in a high arc that I could time who caught it, myself included. I could throw it to myself either 180[sup]o[/sup] from where I threw it or after I rotated 360[sup]o[/sup]. (A 540[sup]o[/sup] or more was harder to do.)
As to just playing simple catch, it took some getting used to. After ignoring the spinning scenery, we also had to get used to the Coreolis (sp?) effect. It couldn’t be ignored.
After getting off of it and playing catch, I had a strange feeling seeing balls travelling in a straight line. :D:D
Once you let go of the ball, it will travel in a straight line until it hits something else. (This isn’t exactly true, it will arc from gravity, and maintain the sideward motion from the carousel, so let’s assume you compensate for that by throwing the ball slightly up and against the spin of the carousel.)
Assume you are throwing the ball from 6 O’Clock on the carousel, and your friend is sitting at 12. If you throw straight across, by the time it arrives on the opposite side of the carousel, your friend will have continued to spin past that point. If you wanted it to arrive in his hands, you’d have to have him sit, say at 2 O’Clock. That way when the ball arrives at the opposite side (12) he will have rotated to that postion.
For you to catch the ball yourself, you have to travel from 6 to 12 in the same time the ball travels across in a straight line. That’s a very fast carousel, and projectile vomitting may be more of a concern.
I’ve actually experimented with this on a Round-Up ride at Canobie Lake Park, IIRC. You can time it out to throw the ball to friends, but it’s a difficult throw and catch. And the ride operators really disapprove.
I’ll have to take more time to read the replies, but at first glance, it sounds like maybe my problem is understanding the Coriolus effect. Personally, I’ve never fully understood how to account for the Coriolus effect.
The Coriolis force is one of the two fictitious forces you need to introduce if you’re trying to apply Newtonian physics to a rotating coordinate system. The other is the centrifugal force (no, I don’t mean centripetal), but that’s generally better understood than Coriolis, so I’ll skip over that here.
OK, when you’re on that carousel, you’re moving at a certain speed. The key to the Coriolis force is that someone at a different point on the carousel is moving at a different speed. Suppose, for instance, that the carousel has a circumference of 30 meters, and that it makes a complete turn every 3 seconds. A person sitting on the edge is then moving 30 meters in 3 seconds, or 10 m/s. A person only halfway out from the center, though, is only travelling 15 meters in the same time, or 5 m/s. Now, suppose that as I pass the 12:00 position (going counterclockwise, 'cause that’s the way that carousels go), I throw a ball at some speed (say, 30 m/s) towards the center of the carousel. The ball then has a velocity of 30 m/s towards the center (from my throw) and 10 m/s to the left (because that was the initial velocity, and I didn’t do anything to it in that direction). Now, when it passes the ring at halfway, it’s still got that 10 m/s to the side, but the observer standing there is only going 5 m/s, so he sees it veering to the side at 5 m/s. In other words, to folks sitting on the carousel, it looks like some force has deflected the ball, and that force is called the Coriolis force.
For a visual answer to your question check out movie 1