Cartwheels

Attach a colored piece of paper to the rim of the cartwheels (or to the bicycle tire) and watch it during movement of the cart (or bicycle). You will notice a strange phenomenon: while the piece of paper is in the lower part of the rolling wheel, it is seen quite clearly; in the upper part it flashes so quickly that you do not have time to see it.

It seems that the upper part of the wheel of the cart moves faster than the lower one. The same observation can be made if one compares the upper and lower spokes of a rolling wheel of some crew. It will be appreciable that the upper spokes merge into one continuous whole, while the lower ones are visible separately. The case again occurs as if the upper part of the wheel moves faster than the lower one.

What is the solution of this strange phenomenon? It's just that the upper part of the rolling wheel of the cart really moves faster than the lower one. The fact seems incredible at first sight, and yet simple reasoning will convince us of this. After all, every point of the rolling wheel makes two movements at once: it turns around the axis and at the same time moves forward along with this axis. There is - as in the case of the globe - the addition of two movements, and the result for the upper and lower parts of the wheel turns out different. At the top, the rotational motion of the cart wheel is added to the translational motion, since both movements are directed to the same side. At the bottom, the rotational movement is directed in the opposite direction and, consequently, is taken away from the translational motion. That is why the upper parts of the cart wheel move relative to the stationary observer faster than the lower ones.

The fact that this is really so, it is easy to understand on a simple experiment, which should be done at a convenient opportunity. Stick a stick into the ground next to the wheel of the standing cart so that the stick is against the axis. On the rim of the wheel, at the top and bottom of it, make notes with chalk or charcoal; marks will, therefore, just against the stick.

Now roll the cart a little to the right, so that the axis moves away from the stick of centimeters by 20-30, and notice how your notes moved. It turns out that the top mark A moved significantly more than the lower B, which just barely backed away from the stick.

So, not all points of the moving wheel of the cart move equally fast. What part of the rolling wheel is slower? It is not difficult to imagine that the slowest of all move those points of the wheel, which at this time are in contact with the ground. Strictly speaking, at the moment of contact with the soil, these points of the wheel are completely immobile.

All that is said is true only for the wheel of a cart rolling, and not for one that rotates on a fixed axis. In the flywheel, for example, the upper and lower points of the wheel move at the same speed.