Attach a colored piece of paper to the rim of a cartwheel and observe its motion. You will witness a peculiar phenomenon: when the paper moves to the bottom of the wheel, it is quite visible, but when it is at the top, it spins so fast that you can no longer recognize it.
When the wheel rolls forward, we have the section: AA’->BB’ |
As a result, it seems that the top part of the wheel moves faster than the bottom part. Similarly, when observing a bicycle wheel in motion, you will notice that the spokes at the top blend together into a continuous band, while the spokes at the bottom remain distinctly separate.
So, what is the mystery behind this phenomenon? The answer is that the top part of the rolling wheel does indeed move faster than the bottom part. Why is that? Each point on the rolling wheel simultaneously performs two types of motion: rotation around the axis and translation forward. Therefore, we have a combination of movements. The resultant motion for the top and bottom parts of the wheel is different. At the top, the rotational motion adds to the translational motion, while at the bottom, it is the opposite. That is why, for an observer, the top part of the wheel appears to move faster than the bottom part.
To demonstrate this, we can conduct a simple experiment as follows: Stick a stick into the ground parallel to the axis of a stationary wheel. Use chalk to mark the highest point (A) and the lowest point (B) on the wheel. Now, push the wheel slightly to the right so that the wheel’s axis is about 20-30 cm away from the stick, and pay attention to how the marks move. You will see that mark A at the top moves significantly more than mark B at the bottom (see the image above: segment AA’ > segment BB’).
