In "bicycle problems" (made famous for example by the book "Which Way Did the Bicycle Go?") the relevant point is the following: If $r(t)$ and $f(t)$ are the points of contact of the rear and front wheel at time $t$, then the vector from $r(t)$ to $f(t)$ is tangent to the curve $r$ and has a fixed length - which is the distance between the bottoms of the two wheels. This is somehow intuitively obvious to me, but I couldn't explain what the reason for this behavior is.
Is it OK to model the bicycle as two individual mass points connected via a fixed-length pole where the "front point" at $f(t)$ drags the "rear point" at $r(t)$ along? But if that were the case, then I would think that the force acting on the rear point would act in the direction of the pole, i.e., the direction of the pole would be the direction of the acceleration exerted on the rear point. Instead, the pole's direction is tangent to $r$ and thus equals the direction of the current velocity of the rear point. Where's my fallacy? Is the model too simple?
Addition: This seems to be related to an older question which, as far as I am concerned, doesn't have a convincing answer.
