03 Stable Wheel

Aim¶

To show how a rolling bicycle wheel “organizes” its stability.

Subjects¶

• 1Q60 (Rotational Stability)

Diagram¶

Equipment¶

• Small bicycle wheel; $\varnothing=40 \mathrm{~cm}$ (or any other wheel or disc).

Presentation¶

• Place the wheel upright on the floor. On release it falls down immediately.

• Then the wheel is released while turning. It rolls over the floor and remains upright for a much longer time.

  The second observation made is that it will follow a curve when it starts falling down. Also notice that the curve it makes, is into the direction of the “falling down” (see Figure 2).

Explanation¶

Figure 3A shows the wheel turning. The rotation is indicated by means of the vector $\underline{\omega}$. Due to some disturbance, the wheel inclines due to gravity: a torque ( $\tau$ ) is acting on the wheel (see Figure 3).

Due to this torque the direction of the vector $\underline{\omega}$ is changed: $\underline{\omega}$ is changed into the direction of $\tau$ (see Figure 3C), so the wheel will make a curve while rolling. This continues because the vectors $\underline{\omega}$ and $\tau$ remain perpendicular to each other.

Also can be seen now that the larger the inclination, the sharper the curve it will make since vector $\vec{r}$ increases, making $\vec{tau}$ larger.