phsysics of unicycling

For my high school Science and Society class my teacher asked me to do my
ISU (Independent Study Unit) on the Physics of unicycling. So far I’m going
to talk about, Unstable Equilibrium, Rotational Motion and Newton’s laws.
At the moment I don’t fully understand Unstable Equilibrium or Rotational

I don’t expect anyone to do my project for me, but if you think I should
talk about anything else please let me know. Also if you could suggest any
books that might help me with any of these topics that would be great. I’m
also looking for things I can do on my unicycle to show the class show the

Jeff Groves


Upright pendulms?

Demonstration: Idling
Natural frequency of system?

Centre of Gravity - in relation to wheel base?
How you have to move it forward to accelerate and centre for constant speed.

Gear Ratios - length of crank/radius of wheel?
Cornering - Gentle leaning method vs hip twist?
Turning circles- 0 to infinity?

Where the other one is…

Remote control unicycle things, I know they are out on the web some where.

The Unicyling Fool

Unstable equilibrium I think refers to the way that a unicycle and rider is never truly balanced (ie in proper equilibrium), but that its constantly wobbling around the same point, making constant small corrections by moving the wheel around under the centre of gravity, so that it falls one way, then back in the other, and so on.
Rotational motion will presmably just mean the speed of the wheel and centripetal force. F = mv^2/r and a = v^2/r, etc. Possible angular momentum as well. Depends on your syllabus.
You could be sneaky and add a bit about acceleration due to gravity and braking forces (from hitting the gound) in trials. Then you’ve also got deformation of solids (the tyre squashing) and force being reduced when it takes longer to stop (force being equal to rate of change of momentum). That might be a but too much for someone who doesn’t unicycle and has never heard of unicycle trials.

Good luck,


I haven’t studied physics in any formal way since I did O Level (now known as GCSE) about 23 years ago, but I reckon my basic physics knowledge would present me with dozens of pages of unicycling-related questions and hypotheses. The subject is too big.

There are 2 simple measureable variables on a unicycle: wheel diameter and crank length. The ratio between these is also a variable. These three variables (2 simple and 1 compound) each affect balance in different ways.

Then there’s fore and aft balance, side to side balance, dynamic balance and static balance…

And changes to balance arising from body posture, arm movement, pedal control…

And the maths of what happens on hills is surprisingly complex.

This subject is HUGE. You perhaps need to narrow it down.

Proper scientific method involves preliminary observation, identification of likely factors and mechanisms, formulation of hypotheses, designing of experiments, completing experiments, analysis of results and refinement of hypotheses… and so on in a continuous quest for a better model of what happens.

Proper scientific method involves changing only one variable at a time, in a systematic way, and analysing the results.

It would be possible to approach the ‘general physics of unicycling’ in a discursive way, but as soon as you try to be specific, and introduce maths, the difficulties will start.

The problems will arise from the variables which are not conducive to gradual amendment - things like the variations in terrain, rider ability, rider attitude - even the windspeed and direction.

In many ways, unicycling is a fertile field for psychological study, rather than physics.

My strong recommendation is that you either keep it discursive and general, or you identify one variable and study its effects. I don’t want to rain on your parade/wee on your chips, but I suggest you speak to your teacher and take advice before starting. You could be biting off more than you can chew. But I don’t know what level of achievement your teacher expects. Perhaps I’m looking at it too deeply. Good luck, anyway.

Feel free to contact me direct on


there is a nice short article about the physics behind a backspin on the following page (the article is in german though):

A backspin is interesting from a physics point of view, because, when properly done, you turn on one spot and switch from forward pedalling to backward pedaling instantly. The article explains why this is possible at all.

Maybe, you find this useful.


English too :slight_smile:

Re: phsysics of unicycling

On Wed, 19 Mar 2003 17:59:08 -0500, “Groves” <> wrote:

>For my high school Science and Society class my teacher asked me to do my
>ISU (Independent Study Unit) on the Physics of unicycling.


In this newsgroup, we’ve had some discussions in the past about
certain aspects of the physics of unicycling. You can search them
using Google Groups, or the search facility on
<> but those are down at the moment.

In either case, use the correct spelling [physics] :slight_smile:

One particular aspect of unicycling physics is addressed on my website
at <>.

Klaas Bil - Newsgroup Addict

"The phrase ““rule of thumb”” is derived from an old English law which stated that you couldn’t beat your wife with anything wider than your thumb. "

If you are looking at the physics of unicycling, one convenient way to break it down for a high school project would be to consider it as two degrees of freedom. First look at why a rolling unicycle doesn’t fall over forward / backward. Then consider how a unicycle doesn’t fall over left / right. The latter has been discussed in this forum quite a bit.
We bounced off the issue a while, but I think we got to the bottom of it eventually.

An article was mentioned a while back that deals with the unstable equilibrium you asked about

The article is a bit advanced for high school and a bit advanced for undergraduates, I’d say. However, if you really want to look into these things, find some text books on controls and look at the way the article deals with the pendulum to control the system. Hope this helps! If you have any questions, post them here early so we can all fight about em’ for a while.

There is a small discusion on physics and unicycling in Sebastian Hoher’s book “Unicycling from beginner to expert”

I remember my applied maths lecturer 6 years back demonstrating an interesting physics prinicple using my unicycle. I can’t recall offhand what it was but it involved pulling the pedal and the wheel rotating in the opposite way from what you would guess.

I’ll try and remember the details because it makes a nice demo. You can ask everyone to guess which way the wheel will move and most of them will be wrong.

Re: Re: phsysics of unicycling

Yeah! I thought this was gonna be a thread about Uri Geller bending cranks!

Apparently, this is apocryphal. The Straight Dope.

Re: Ideas

This one is cool!

Re: Re: Ideas

Thats the one!



Here is a picture demonstrating what peter.bier was saying. The wheel rolls left. See if you can figure out why :slight_smile:


Re: phsysics of unicycling

bbraf wrote:
> there is a nice short article about the physics behind a
> backspin on the
> following page (the article is in german though):

The same article is available in english at

Best wishes,

| ~ ~ |
(- 0 0 -)
| |
| Wolfgang Strößner |
| |
| Oooo. |
±------.oooO-----( )----------+
( ) ) /
\ ( (

I just tried that wheel turning thing and guessed the wrong direction!
It’s a really nice and bizarre little demo.

that loonycycle is made by a school 10 minutes away from me!

I too am doing a presentation on the physics of unicycling. I will attempt to cover the following topics:

  • Rotational Motion: angular velocity, acceleration, and momentum
  • Precession
  • Equilibirum (or the lack of it)

Rotational motion is motion around a fixed axis. Since every point of the body (in this case the wheel) moves in a circle, the wheel has a constant angular rotation.

Angular postion: Theta = s/r
Angular velocity: Change Theta/Change Time
Angular acceleration = Change angular velocity/change time

r = radius
s = arbitary axis
theta = angle b/w S and R

Torque is another important conecpt in rotational motion. Torque is a force applied to a rigid body that rotates around the axis (pushing down on the pedal and crank arm is torque). To find torque, use use the formula:

T = RF sin theta

r = radius
f = force
theta = angle b/w two

(this explains the “dead” position when the pedal is at the very bottom sin 180 = 0)

Wheels have rotational and translational (linear) motion, since it rolls and moves foward in a straight line.

Linear motion:

Top, middle, and bottom of the wheel has the same velocity and direction

Rotational Motion:

Top and bottom have same angular velocity, butdifferent direction (tops rotates “forward,” bottom rotates “backwards”) The middle has no angular velocity.

When ou add these two forces together, the bottom has no velocity, the middle has velocity equal to v, and the top has velocity equal to 2v. Therefore, if you take a picture of a rotating wheel, the top of the picture is blurred, while the bottom is more clear.

Ok one last topic. The law of conservation of angular momemtum states that if no external torque acts on a system, its angular momentum will not change. This is precession. If you roll a wheel (such as an UW wheel or impossible wheel) it will rool straight and not tip over.

Well I hope you can make sense of this. If not, I’ll try to clarify it for you when my brain is more active.

Freaks from Oxford?

so why does the wheel roll left? i would assume the system is much like a yo-yo. well, i suppose that the yo-yo will roll toward the direction of the pull, simply because that is the direction of the force, but…what about the other way?! :thinking:

I think it’s demonstrating countersteering.

The following Google search will give you more info on countersteering.
<countersteer OR countersteering bicycle - Google Search;
There are even some physics discusions on countersteering in the Google results. The Google search is on “countersteer OR countersteering bicycle”.

Countersteering is not intuitive. It doesn’t make sense unless you happen to understand what is really going on when you turn a bike, motorcycle or unicycle. Countersteering works on a unicycle too. If you want to do a sharp tight turn you initiate the turn by countersteering.