Problem — Bicycle and gyroscopic effect

Problem

Explain why a stationary bicycle falls over, but a moving one stays balanced. Refer to the angular momentum of the wheels.

Solution

When stationary, the bicycle is an unstable pendulum: the slightest tilt produces a moment of the weight that makes it fall.

When moving, the rotating wheels possess a horizontal angular momentum $\vec{L}$, directed along the wheels’ axis. When the bike tilts, the weight produces a torque $\vec{\tau}$ perpendicular to $\vec{L}$. By the law $\dfrac{d\vec{L}}{dt} = \vec{\tau}$, $\vec{L}$ does not fall but rotates (precesses): the result is that the handlebars automatically steer in the direction of the fall. This shifts the contact point under the centre of mass and rights the bike. The cyclist continuously corrects and balance is maintained. It is the same gyroscopic effect that stabilises a spinning top. $\ev{\text{wheels with } \vec L \text{ horizontal} \Rightarrow \text{precession causes steering} \Rightarrow \text{self-balancing}}$

Links

Topics: Rotational dynamics Concepts: Angular momentum · Torque Objects: Rotating disc