The physics
A wheel that rolls without slipping has its contact point still for an instant. The whole wheel turns about that point at ω = v/R.
speed of a dot = ω × (its distance from the contact point)
So the top moves at 2v and the bottom is still. A dot level with the centre moves at v√2, at 45°.
When the wheel turns by θ, its centre rolls Rθ. A coin that rolls round a fixed coin turns (R + r)/r times.
To push a wheel over a kerb, take torques about the kerb's edge.
F(R − h) = mg√(R² − (R − h)²)
A roller hits a step. Its L about the edge stays the same through the jolt. Then energy lifts it.
Mv(βR + R − h) = (1 + β)MR²ω′ ½(1 + β)MR²ω′² = Mgh