Why do we fall down when the bicycle slows down?

Question

My question is: It is easy to balance a bicycle when it is moving at a fairly high velocity, say 7 m/s or 25 km/hr. But when a bicycle slows down, it is hard to keep it upright, and the person riding it may thus fall down! Why?

Answer 1

When a bicycle is moving at 7 m/sec the wheels are rotating at a substantial angular velocity in radians per second. Not only do we have in the motion of our system conservation of linear momentum, we also have conservation of angular momentum. We have the inertial mass of the bike and rider resisting accelerations due to external forces. We also have the angular moment of inertia of the bike wheels resisting accelerations due to external forces.

When the wheels are barely moving the angular moments of inertia become very small and external forces have greater effects on the velocity of the bike and rider or the system has the least resistance to change.

One can get a quantitative feel for these moments using the moment calculation for a hoop of constant mass density rotating about a central axis perpendicular to the hoop as a model of the bike wheel

One can also get a feel for the imbalancing forces on shifting the center of mass of bike and rider or changing the friction from asphalt to gravel. Making these changes while the angular moments are large result in little change in velocity from our imbalancing forces. Making these changes at slower speeds with reduced inertia and angular momenta results in large changes in velocity from the same imbalancing forces.

You can actually feel the bikes resistance to force- spin the wheel and then try to tilt the bike wheel out of the plane it is spinning in....it resists your efforts to tilt it. Do the same with the wheel not spinning and there is little resistance to tilting the wheel.

We see this with a gyroscope.