The physics of tops
October 9, 2011 10:09 AM   Subscribe

Simplified technical explanation for how tops that flip themselves over work?

I showed a friend one of those tops that flip over when you spin them. She asked me how it works, and I thought I could figure it out and explain it, but I ended up just babbling something about moment of inertia, weight distribution, instability, and the trajectory that each segment is trying to take... and then I realized that no, I can't figure it out on the spot and I needed to come up with a clearer explanation. So I thought this would be a good place to get a technical, but simply stated explanation. How would you explain the mechanics of a self-righting top?
posted by molecicco to Science & Nature (4 answers total) 1 user marked this as a favorite
 
It flips because the center of mass does not coincide with the geometric center of the sphere. It also changes the direction of rotation.
posted by weapons-grade pandemonium at 10:18 AM on October 9, 2011


Well, I suppose the direction of rotation doesn't really change from the point of view of the top. But it does for the viewer.
posted by weapons-grade pandemonium at 10:22 AM on October 9, 2011


Well, I don't think you have to feel too bad about not being able to crack it immediately, because it seems to be a fairly complicated interaction between a few different forces.

The simplest and clearest explanation I found was here. The crux of the explanation:
The center of the curve described by the bottom of the top is higher than the center of mass. The curve will pull its center towards the lowest possible point – much the way the curve of an egg, if placed on end, will fall sideways and rest on its flatter side, pulling its center down. Meanwhile, an untethered object, if spun, will rotate around its center of mass. The center of mass has been lifted up and to the side when the top falls sideways.

Usually, when an object spins, the point that it's spinning on – the point of the object that makes contact with the ground - is directly below the object's center of mass. That contact point is steady on the ground and doesn't move. The object spins around it.

When a tippe top spins, because of the switcheroo trick the curve pulls, the point of the object that touches the ground is not below the center of mass. It is below the center of the curve, slightly to the side of the center of mass. The object still must spin around the center of mass, though, so the contact point of the top gets dragged around in a circle. The motion of the spinning top pushes that contact point down and to one side. Anyone who has dragged an object along the ground knows the feel of friction. It counteracts the force one puts on the object. If the spin of the top is pushing the contact point down and to the side, the ground is pushing the top up, and to the opposite side. The top feels a force pushing up and backwards.
That upward force is what makes it possible for the top to lift its center of mass up (which answers the question most perplexing about the top--how is it able to lift its center of gravity). You'll want to read the rest and look at the photo here.
posted by flug at 10:36 PM on October 9, 2011


It also changes the direction of rotation.

Just to clarify that, from an outside reference frame--say the earth reference frame as determined by the direction of gravity--the top will spin the same direction the whole time. If it starts out spinning clockwise, it will stay spinning clockwise.

However from the reference frame of the top itself--defined, say, by the axis from the top through the little peg--it's different. It starts out rotating around that access in one direction (say, clockwise), then midway through its little trick, just when the peg is close to horizontal, the rotation around that axis slows, stops, and reverses. And the tippetop ends up spinning fast in the opposite direction (counterclockwise if the initial direction was clockwise) around that axis when it is standing on end.

Of course, at the moment it is slowing, stopping, and reversing spin in that axis it is spinning very rapidly around a different axis.

So from 'our' perspective the tippetop always spins in the same direction, but from 'its' perspective the spin reverses direction right in the middle of it's little maneuver.
posted by flug at 12:57 AM on October 10, 2011


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