Aristotle wheel paradox, paradoxo da roda de aristóteles

It seams like circles are equal? Or not? Watch the video Aristotle's wheel paradox funny trick
#veproject1

Paradoxo da roda de aristóteles, アリストテレスの車輪のパラドックス
Aristotle wheel paradox

[lucianoboscolo]

It's a very nice optical effect. The reference point is where the disc touches the table. That's where the disc is really rotating to. The two inner discs are just sliding over the horizontal cords.

[TheInwardseye]

The angular velocities are the same and so they traveling the same number of degrees per second at any given moment. The tangential velocities are different, the smaller circle travels more slowly in the same period of time, its circumference is therefore shorter

[mccurrycreations]

The wheel isn't rotating on either of those circumferences.  It's rotating on the wheel's circumference.  The other two circumferences are technically skidding into position rather than rolling. if you cut the wheel down to the circumference of the inner circle and rolled it across that top line, it would actually come back to the mark before it hit the end of the track.  In fact... considering that the inner circle is roughly half the diameter, it would probably make two full rotations by the time it got to the end.

[franksalterego]

The two inner circles are "skidding" on the lines.

Frank

[georgegrund]

This is why people who live in the center of the earth live seven times as long. Ha ha ha

[danarredondo]

There is a third circle.. Where the wheel touches the table..

[istantch]

neither one "rolls" over the strings but "slips" making it a different length, only appearing the same ...

No it means that the distance between the 2 lines is the amount of difference between the 2 circles

[igxniisan]

0:37, this pucking doesn't mean that the circumference of the two circumscribed circles are the same, well despite of the fact that both the circles have exactly the same “angular velocity”, the circle inside has lower “tangential velocity” than the circle outside, hence if you rotate the circle like that, the inner circle is actually “sliding” on the upper track, not actually rolling, which means you are forcing the smaller circle to move at a higher speed than it's very own tangential velocity, welp to say it precisely, the tangential velocity of the bigger circle is responsible for the linear velocity at the centre of the whole structure in the direction opposite to that of tangential velocity. Thus the smaller circle circumscribing the bigger one is forced to move such that it's center always matches the position of the bigger circle's center, hence the smaller circle, despite of having a lower tangential velocity tends to slide on the upper track such that the linear velocity of its centre matches that of the bigger one. Now yes both the notches matches perfectly after rolling it 1 rev, that's because the “angular velocity” is same everywhere inside it. Hence this ain't even a paradox, rather stupid illusion xD

[wesbat]

You assume we are measuring their circumference, but in fact this measures degrees. Each circle has 360 degrees, no matter it's size. The larger has more surface area and rolls faster, the smaller rolls slower. In the end, their difference in roll speed balances out their varying circumferences and both reach full rotation at the same time.

[andreschoen]

Hint - watch the center point.
It travels from one end to the other & clearly has a tiny circumference.
But it also only completes 1 rotation.
Wonderful Brain Fudge cheers.

[gonzaloglz]

Inner circles appear to be "rolling" on the string, tricking your eye into thinking the string length and circle circumference must be the same length. In fact the circle is "sliding" along the string as it rotates. Think of it as a skidding spinning wheel. It travels further than it rolls. The black string and black lines help disguise the discrepancy.
Great illusion!

[deathsheir]

It comes down to the distance from the center.

Take the two circles, and separate them and put them on different axels . Mark the circles at a single point near the very edge, then allow the two circles to rotate at 1 revolution a second. That means the mark you made, must return to the same position every 1 second.

Despite those marks you made rotating at the exact same speed, the axel on the larger circle, has to spin faster than the axel of the smaller circle.

Thus when they are fixed on the same axel, so neither can move independently of each other, on technicality one circle is moving faster than the other, to maintain its relative location.

It was a paradox at the time of Aristotle, because they didn't have the knowledge we do now. Thanks to our knowledge now, we know that there is no paradox.

Still very cool to see.

[hauikanamu]

The upper circle not true to its circumference when subject to the large wheel. The upper circle is essentially sliding along the length of string.

[BayareaJay]

The distance of the circumference is not equal due to their being two "strings" separated by a 1-2 inch difference.

[FenixDown]

its based off the single circumference or the outside diameter of the wheel in witch the 2 circles are drawn onto. if you were to use 2 wheels with their own diameters, one would travel further

[mattg]

The inner circle does not travel along the line at the same speed, you just can't see the effect. If you tried this with a chain/cog set up instead of a smooth, then it would not move at all (the cog on the inner circle would act as a brake. If you look at the length of the circle perimeters, you can see that it couldn't be any other way

[Mezzo_Roo]

no. its actually that its one circle with 2 circles printed on it. veporject1, how could you be so blind?

[GhostEmblem]

Because the two drawn circles are rotating with respect to the center of the 3rd circle, the circular board they are drawn upon they are actually rotating at different speed to each other with the larger covering a greater distance in the same time.

If you were to stick the strings to the board where the larger and smaller circles are drawn you'd find the neither have a circumference the length of the string and the length is in fact the circumference of the board which is the true distance both points traveled in the same amount of time.

[LazlosPlane]

That is a wheel paradox.   I wheely am baffled.   I would like a wheel explanation.  Get wheel.