This Doesn't make ANY SENSE - Aristotle's Wheel Paradox

STL:

Aristotle's wheel paradox, described in the Greek work "Mechanica," posits that two concentric wheels, one larger than the other, when rolled, should travel the same distance, even though the larger wheel's circumference is greater.

Here's a breakdown:

The Setup:
Imagine two concentric wheels, one large and one small, attached to a single axle.

The Paradox:
When the larger wheel rolls a distance equal to its circumference, the smaller wheel, also attached to the axle, should also travel a distance equal to its circumference, even though its circumference is smaller.

The apparent contradiction:
The larger wheel's circumference is greater than the smaller wheel's, yet they both appear to travel the same distance in one full rotation.

The Resolution:
The paradox arises from the fact that the smaller wheel, while appearing to roll, is actually sliding to compensate for the larger wheel's greater circumference.

Analogy:
Think of it like a polygon rolling. As the number of sides of the polygon increases, the "hops" become shorter and more frequent, eventually becoming a smooth slide, as seen in a circle.

In essence:
The paradox highlights the difference between the circumference of a circle and the distance a point on the circumference travels when the circle rolls

[Bennoah]

It is simple. It is because when they are connected they are traveling forward on the circumference of the larger wheel. It is no paradox it is an illusion.

[snakester]

It’s because they’re connected, if they were rolling on the track separately, the small circle would roll normally

[SHYAMBABU-lokb]

When the wheels are rolling separately it is pure rolling but when small wheel is attached to big wheel the small wheel is slip rolling.

[CrazyK]

There is NO slipping or sliding or dragging or skipping of anything. Nothing slides. Both rotate around the center point on their own plane. U tube has an awesome explanation if you would look it up. There is too much to explain here in the comments. Go see.

[xXTrentXx]

Just make everything the same but make the big wheels diameter 2mm less so the small wheel is in contact with the track properly, when you roll it you should get the opposite effect 😁

[dooliant]

It’s an illusion - There is no small wheel! It is one large wheel when the 2 are joined.

[navtektv]

The larger wheel is pushing the smaller wheel forwards to cover more distance than just what it would cover with just rotation power. Its sliding the wheel forwards.

[vixynfoxtail]

It's simply that the small wheel is translating in a "sliding" motion instead of as a translating as a ratio of its circumference... it makes perfect sense...

The dot in the middle translates as a straight line

[fbi]

The smaller wheel is incorporated within the circumference of the larger wheel and is no long an individual factor.

[michaeldavis]

Neat but simple and there’s no paradox. The large wheel is carrying the small one so it’s of course going twice as far. The Tardis is impossible people lol

[izaiahgladiator]

He basically turned the circumference of the small wheel into the same circumference as the big wheel doubling the distance traveled if he set the smaller wheel on a track and the big wheel was connected the big wheel would travel 2 times as fast

[Strmkng]

It depends on which wheel is actually being held up by the measurement device. This could have been done in a way in which the large will rotated at the small wheels distance

[nycronezeith]

It is also known as illusory rotation. It is where a small disk reacts and acts like a large one. Let me explain why the small disk is in the center of the large disk, both run at the same speed and in the same direction, thus creating the same distance. However, when the disks are divided and separated, the distance and the indicated speed change. Welcome to illusory rotation.

[TybreSnell-ub]

The circles become one look at it like there is no small wheel the big wheel takes over the smaller one because the circumference transfers from small wheel to the big one

[thejimlad]

Same concept as a open differential to a locked differential on a car when cornering is it not let them move freely and they will move there own time big wheel is forcing the little wheel to skip in its rotation

[dhooterchoor]

Radius increased which leads to increase in Circumference. Does education banned in USA 😂😂😂

[tejinder]

It becomes one piece when attached to bigger wheel.

[semirnukovic]

Nah nah nah. Here is the answer, are you ready? Oh boy… It’s about the travel distance. The small wheel has a shorter range because of its smaller diameter, of course. Just like Tape. And the bigger wheel has a larger range. And both connected together make the smaller wheel actually travel at the same distance as the bigger wheel.
Because the red line travels at each point but the speed is being controlled by the contact of the outer edge of course. Just like a car wheel and any other wheel.

[jasonbalenweddingfilm]

large wheel is rolling on the floor. Small is on top of the ruler

[starmaker]

Connect them through a ball bearing and it won't work anymore as it just works, because the smaller wheel slips over the surface, not?