03 Stable Wheel

03 Stable Wheel#

Aim#

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

Subjects#

  • 1Q60 (Rotational Stability)

Diagram#

../../../../../_images/figure_0113.png

Fig. 259 .#

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 260).

../../../../../_images/figure_185.png

Fig. 260 .#

Explanation#

Figure 261A 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 261).

../../../../../_images/figure_237.png

Fig. 261 .#

Due to this torque the direction of the vector \(\underline{\omega}\) is changed: \(\underline{\omega}\) is changed into the direction of \(\tau\) (see Figure 261C), 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.

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