When a round coin rolls down a聽slope, it stays upright, so why does聽a 鈥渟quare鈥� coin sliding down a聽slippery slope soon fall over?
Ron Dippold
San Diego, California, US
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The round coin has two related advantages, rotational inertia and being a mini gyroscope.
Let us take the square coin first. If it is sliding down a slippery slope, narrow side leading, there is little to prevent it from tipping over. It is sitting on a narrow edge on a slippery surface, so it is inherently unstable. All it takes is the slightest variation in the slope to make it fall over. Basically, there is no reason for it to stay upright 鈥� falling over is just as good as going forwards.
Now, consider the round coin. It is a freestanding wheel. Once it picks up speed, it has rotational inertia, and an object 鈥渨ants鈥� to keep travelling in the direction it is currently heading unless there is an outside force like friction (Isaac Newton鈥檚 first law of motion). Even if your slope flattens out, the coin will keep rolling quite a way until friction brings it to a stop.
Second, it is now a gyroscope. Any spinning wheel resists rotating in any axis other than the one it is already turning in (Newton鈥檚 first law again!). The easiest way to feel this yourself is with a detached front bike wheel or by using some wood or a box to raise the front wheel of a bicycle off the ground. Try turning the wheel left and right, then get the wheel spinning as fast as you can with your hand. Now try turning the wheel left or right again. You will feel the gyroscopic force of the wheel resisting you because you aren鈥檛 turning it in the direction of the rotational inertia.
This is used as a stabiliser in many applications, such as with film cameras. So, the rotating coin actively resists turning left to right (turning) or top to bottom (falling over), and it 鈥渨ants鈥� to keep rolling. It is a rolling machine! The only way it will fall over is if the slope is so uneven that the coin is stopped or tilted too far to recover.
Again, we can use the bicycle as an example. Get on a non-moving bicycle and, with your feet off the ground, try to stay upright. Pretty dang hard, right? I can鈥檛 do it. This is your square coin. But as soon as the bicycle is rolling just a few kilometres per hour, staying upright is trivial. Your coin is one of the wheels,
Guy Cox
Sydney, Australia
When you spin a top, it stays up, but once it stops, it falls over. That is the gyroscopic effect: rotating objects resist changing their angle of rotation because it changes their angular momentum. Gyroscopes are used in all sorts of things, from Segway scooters to navigation systems.
In the case of your coin, so long as it is rotating, it will stay upright. But there is nothing to keep your square coin upright, so over it goes.
David Haller
Via Facebook
Let me put away my frisbee and yo-yo, hop on my bike and head on over to answer the question.
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