Dear Esprit,” –said my good friend, Professor M. Boleslavsky, who taught the course “Theory of Electrical Circuits” at the Polytechnic Institute and (at the request of the Dean of the Faculty of Physics and Mathematics) at the University, while teaching a course in “Theoretical physics”, – “today we had a debate in the faculty room about the simplest thing. And I suggest you be the arbiter”.

Dear Professor, – I replied, – thank you, the offer is more than complimentary, but HOW can I, a person without any scientific titles and degrees, be an arbitrator in a dispute between highly qualified specialists? Physics and mathematics professors at the university!

Try it, — the professor replied with a touch of irony. – Are you ready to listen to the task?

So, the most common wheel. We spun it by holding it by the axle in the air, and then we threw it onto the road and it rolled on its own.

Why is the wheel moving forward?

Let’s look at the forces acting on it:

The weight of the wheel is directed vertically downward from its center of gravity. It will not move the wheel horizontally.

Centripetal and centrifugal forces CANNOT make the wheel move forward. They are directed to the center and away from the center of rotation by radii.

The only “horizontal” force that acts on a rolling wheel is the FRICTION force applied to it at the point of contact with the road. It is directed forward, that is, against the linear velocity of the lower point on the wheel, but the friction force cannot make the wheel move forward.

Let’s ignore the air resistance, because it also does not help the wheel to roll in any way.

So, it can be seen from the diagram of all forces that not a single force is capable of moving a wheel along the road! Nevertheless, IT’S ROLLING!

So why is it rolling?

We’re not pushing it, we just threw it spinning on the road.

From the tone and slight smile, I immediately sensed that there was some kind of trick here. But which one? All the professor’s arguments seemed to be quite fair and logical.

So, WHAT really makes the wheel to move forward?

After a moment’s thought, I answered.

The very approach to the topic is wrong!

Formally speaking, there is no pushing force other than the friction force, which simply stops the point of the wheel rim that touches the ground.

But the wheel, if we hadn’t thrown it on the road, but had held onto the axle, would have continued to rotate BY INERTIA!

Now let’s see WHAT’s happening on the road.

The wheel rotates by inertia, as we have spun it and given it the kinetic energy of rotation. Once on the road, the wheel continues to rotate around the axis, but the AXIS OF ROTATION has now moved to the POINT where it TOUCHES the ground, and the wheel continues to turn by inertia! So it tries to rotate around a new point of the “axis” – the point of its adhesion to the soil, and therefore there is a FORCE of INERTIA, which all the time rotates it around continuously emerging new centers of rotation – the points of contact of the wheel with the road. That’s the reason why it’s rolling. By throwing it on the road, we have created a situation in which the wheel “tends” to rotate around its axis, but cannot, since one point of its rim is stopped by friction! And the accumulated kinetic energy of inertia is available, and its rotation continues around all new “axes” – points of contact with the road. It kind of “circles around” the roads. This creates a force applied to the wheel axis and directed forward.

In any car, the engine does NOT move the entire mechanism forward or backward, but only turns the wheel axis through the transmission. However, since the lower part of the wheel is in contact with the road surface, the wheel turns NOT just around the axis, but, involuntarily, around new axes of rotation – its points of contact with the road, and this moves any mechanism forward or backward.

The wheel “throws” the road back and thus rolls forward.  

My explanation caused a moment of surprised silence.

How come?

The professors argued for almost half an hour about the reasons for its rolling, but they did not come to a conclusion. And here, a person with a primary education suddenly gives a simple and natural explanation in a few minutes. And, by the judgments, it is correct.

And the reason, again, is the approach. The professors considered this ordinary phenomenon from the point of view of formal mathematics: Forces, their decomposition into components, diagrams of forces and velocity vectors, and so on. But it was necessary to simply consider the common physical sense of the phenomenon. And everything fell into place without any formalism or vector diagrams.

16 II 2020