When The Coin Spins

A coin is spinning on a table, and then it - what?
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click If a point on the edge of the coin was bouncing, it would move in a series of parabolic arcs with abrupt changes in direction at the bounce. Since the coin is rotating with the center of mass at a slowly descending height, the motion of a point at the edge is approximately sinusoidal.

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Jeff Samples 11 1. To summarise, relating to the original question: Dissipation of the energy comes from rolling friction and from slippage between the coin and the surface. Viscous effects in the layer of air between the coin and the table are of less importance in contrast to Moffatt's original finding. There is a relationship between the angular velocity of a fixed point on the coin i. The two are proportional in steady-state, with the constant of proportionality being given by the ratio of the horizontal distance between the axis of rotation and the centre of mass of the coin to the radius of the coin.

This distance tends to zero as the coin settles, cancelling the divergent frequency of the precession.

As previously discussed, this is not a bouncing but rather a rolling motion. Nonetheless, it helps to draw parallels with bouncing to understand why the period decreases with time.

The Math Behind a Spinning Coin

Picture a bouncing ball; with each bounce, it loses energy just as the coin continually loses energy as it rolls. Because the amplitude of the bounces gets smaller, the period of the bouncing motion gets smaller too.

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This is complemented in the case of the coin by the increasing vertical acceleration as the precession frequency increases. You can also find a listing of some more articles on the phenomenon here. Sign up or log in Sign up using Google. Sign up using Facebook.

A spinning coin explained

As previously discussed, this is not a bouncing but rather a rolling motion. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site the association bonus does not count. When you write hamiltonian and canonical equations probably you will get some coupled non-linear partial differential equations which are worst combinations to solve. Spinning the ring in a vacuum had no identifiable effect, while a Teflon spinning support surface gave a record time of 51 seconds, corroborating the claim that rolling friction is the primary mechanism for kinetic energy dissipation. As the period of the spin around the spin axis increases, the period of the precession increases. Personally I think that it is a complicated but somehow treatable problem with a lot of patience. When you spin a coin on its side, it slowly loses energy and starts wobbling around.

Sign up using Email and Password. By using our site, you acknowledge that you have read and understand our Cookie Policy , Privacy Policy , and our Terms of Service. It does not stay at just one point on the table but its point of contact with table changes with time.

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I was trying to explain quantitatively this but I am stuck at how to take frictional torques into account. Any help will be appreciated. I think that if you spin "perfectly" i. This motion is unstable though, so, the axis tilt a little bit and this cause a rotation in the axis itself, the precession.

Euler's Disk

I don't know your level of knowledge, but for a complete description you need knowledge of Hamiltonian dynamics, rigid body and Euler angles, so basically a course of classical a. A very common, related, problem is the problem of the spinning top, the difference here is that the contact point is material, so there you have to see if you have to see if the contact point slips or not if not, it creates a rotation in the axis normal to the coin.

Personally I think that it is a complicated but somehow treatable problem with a lot of patience. There is no easy way to model a spinning coin and calculate these observations. It slows down mostly because of air resistance and friction here you must take velocity dependent friction-angular velocity in your case- and it moves due to the combination of torque of gravity a.

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Velocity dependent frictions generally gives you non-linear differential equations which are often very hard to handle. When you write hamiltonian and canonical equations probably you will get some coupled non-linear partial differential equations which are worst combinations to solve.

Moreover, after it slows enough, contact point on the coin will start to move and after that time you should consider rolling friction. But ofcourse thats not what you asked for: Dictionary and thread title search: A coin is spinning on a table, and then it - what? Previous Thread Next Thread. I'm trying to describe what a coin spinning on a table does when the spin degrades into that low, waffling, rapid shallow spin that occurs just before the coin stops and lays flat.

I can't imagine what verb could possibly illustrate this final part of the spin.

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In frustration, I've tried to convey it with the sound of those final shallow rotations: He walked over to his pint-sized dining table, whispered his call, and flipped the quarter two feet into the air. It came down fast, hit the tabletop, bounced up two inches, landed spinning on its edge, clattered and lay flat.

I'm unsatisfied with this but not sure I can do any better.