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I’m mainly just posting this here as a placeholder until I finish my comments. But I saw this and am curious:

I’d like to do a full workup on the physics of this thing building on my newfound partial understanding of wheels.

But here are some questions I’m thinking about:

Let’s let the system be the rider and the cycle.

• What provides the torque that keeps the rider from falling over? I know it’s somehow provided by the engine, but this isn’t an external torque, so we need an external torqe, of the road, I assume.
• Which begs the question, if this thing were being used on ice, could it not prevent the rider from falling over? I think that’s a yes.

I’ll think about this some more and post more in a few days.

Let’s start by assuming that the unicyclist is traveling at a constant speed on level ground, at a slow enough velocity to neglect the drag force of air.

FBD for unicycle moving to the right at constant velocity.

Ok, other than the fact that the ground is exerting two horizontal forces on the cycle (friction and traction), this isn’t too exciting just yet.

To really get at what’s going on, we need to look at forces and torques.

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