Riding forward, spinning 180 degrees around a vertical axis and riding backward in the same direction you started riding forward is called a backspin. Frontspin is just the same, riding backwards, spinning 180 degrees to riding forward. Then there is the riding spin. It means riding forward, performing a complete rotation (360 degrees) around a vertical axis and riding away as if nothing had happened. Backward riding spin is exactly the same, but riding backwards.
In the sequel we will talk about backspin resp. riding spin. All to be said is valid for frontspin and backward riding spin as well, when swapping the words forward and backward.
Beginners often perform these spins by riding in a circle as small as possible for a riding spin, and doing a 90 degrees arc, stopping, accelerating to the back and doing another 90 degrees arc immediately for the backspin. If the the radius of the circle resp. the arc is small enough and stopping and accelerating is performed quick enough that looks quite ok. But nothing more.
Everyone who ever witnessed a real spin in contrary to the things described above will admit that there is a huge difference. One can perform a backspin or riding spin in a way that it looks like twisting at one point and then riding away backward or forward. When it is done properly, it doesn't seem like riding but more like floating and then twisting. Twisting is indeed a very natural movement when floating...
Till now, none is able to float with a unicycle. So there has to be another explanation. Everyone knowing little about physics will admit that due to basic theorems about preservation of momentum it is not possible to generate rotation from nothing. The area of the tire touching the floor won't provide enough friction or adhesion to being able to be used for initiating rotation. So, where does the momentum come from?
A spin is not performed as spontaneously as may look like. In order to perform it the rider does the following: riding a huge arc (with a diameter of several meters), then suddenly blocking the pedals. This causes a rotation in the direction of the arc. After half or full a rotation he releases the pedals and goes on riding. That is performing a backspin resp. riding spin. When doing the arc with a radius large enough and starting it just before performing the spin, then it's nearby invisible for spectators, and it looks like the spins are performed from riding in a straight line. Of course it's not such easy as it sounds here. Except of blocking your pedals, you have to tilt somewhat to the back as the wheel - because of not floating at all but having adhesion to the floor - can't rotate while spinning horizontally, so there's some acceleration - or spoken practically, an emergency stop -, so the rider will be thrown to the front. That's a useful fact, as after finishing the spin, you are tilted to the front (according to the direction of movement, when doing a backspin that means tilted to the back according to your body). You will need this tilt for speeding up for compensating the loss of speed. It is supposed - at least from the view of the audience - to ride with constant speed. That breaking and speeding up when performing spins like beginners do has nothing in common with breaking and speeding up here. It's only needed to compensate losses from friction of tire and floor. As long as the wheel is twisting it doesn't rotate, but only slides, and it won't do that very well. When seeing someone performing spins fluently, it's for sure, he practiced a lot for that.
This is not a unicycling work shop, but I want to explain the theoretic background of spins. So let's neglect the practical aspects and deal with theory.
It's easy to set up an experiment in order to proof that the principles described above really do work. Take a string and attach it to a pen to balance the pen horizontally, with one end of the string going upward, the other one going downward. Take these two ends (one hand above the pen, the other one below in order to get the pen hanging between the hands, see illustration). Now turn around and stop suddenly. The pen will rotate.
The reason for that can be explained. A pen has a length, like a unicycle.
Considering the pen, it's the distance from the front end to the back end.
Considering the unicycle, it's the diameter of the wheel (assuming, the seat is
shorter than that). When moving the unicycle on a circle like shown in the
illustration, at an arbitrary but fixed time the point at the front end of the
wheel p1 moves with speed v1 in a direction tangent to
the circle (we always assume speed as a vector, so the term speed means the
absolute value of the speed as well as its direction). The point p2
at the back end of the wheel moves with speed v2 in a tangent
direction as well. It holds | v1| = | v2|, but
v1und v2 are not parallel.
When blocking the pedals, the unicycle gets accelerated in its point of gravity p. Let g be a speed in point p, in a direction tangent of circle s, with negative sign according to v1 resp. v2 (that means, g and v1 resp. g and v2 intersect in an angle > 180 degrees) and with |g| = |v1| = |v2|. When stopping the forward movement of the unicycle completely by negative acceleration (that means, the acceleration is exactly as strong as it needs to be to speed up the unicycle from stillstand to speed g), then p1 moves with speed w1 = v1 - g and p2 moves with speed w2 = v2 - g. The normal part (referring to s) of w1 and w2 are additive invers. So there will be a rotation around p, the point of gravity of the unicycle. Similar considerations are true for any other point q1 of the unicycle and the point q2 = 2 p - q1.
We made several simplifications here:
The unicycle was considered to be symmetric. Of course that is not true in reality. But unicycles and their riders are more or less symmetric. So the deviation from the truth may be neglected.
A unicycle is straight, not bend. That means, the points p1 and p2 are not situated on s. But the deviation may be neglected, as the diameter of the wheel is very small compared to the radius of s.
By tilting before resp. after blocking the pedals the point of gravity will move. That fact is not negligible. Because of not having access to data about time and intensity of tilting, I wasn't able to respect it.
Pedals can't be blocked in no time. It's an event, that takes some time. In reality, stopping the rotation of the wheel and accelerating again takes all the time of spinning. That will influence the whole thing. As before that perturbation had to be neglected due to a lack of data.
There may be other perturbations not mentioned yet, e.g. friction of floor and tyre, friction within the bearings of the unicycle, air resistance and the fact that unicycle and rider move all the time (not only seen with the eyes of a fixed spectator). Unicycle and rider are not a fixed thing, but they permanently change their point of gravity. Then there is some inertia resulting from the rotation of the wheel. All these things and many others have been neglected.
Concluding I have to admit that some of these perturbations may, all
together will influence this sketchy model. So don't rely on quantitative
results. But I think, I was able to provide a qualitative explanation of the
origins of that rotation about a vertical axis. You will get a glue of the
inaccuracy of the model, when considering the speed of spinning. Due to
preservation of momentum, according to that model a backspin takes exactly as
long as it takes to ride half the circle s with constant speed. At a speed of v
= 15km/h and a radius of s of r = 4m we obtain a time t of some over 3 seconds
(t = π r / v). In reality it needs much less time (below one second).