If that were the case the friction would be cumulative and would slow the ball progressivley over the duration of the curving balls motion and therefore each meter on the straight run would not correspond with each quarter mark on the curved run.jacmac wrote:I don't know about the math, but the ball in the curved tube is being slowed down by the curve compared to the ball in the straight line tube.
MilesSucksWithMaths wrote:Let us say points A and B are on a circle, and you wish to travel from A to B. It seems like the simplest
thing to do would be to take the path c , since it is the most direct. You just cut straight across on the
hypotenuse. In fact, that is what the ancient Greeks assumed, and their original assumption has skewed
this problem ever since. It is still the assumption today. Mainstream physicists and mathematicians
still assume the circle is composed of a lot of little c-paths. They make the c -paths very tiny and then sum them, giving them the circumference of the circle. But what I have shown is that they have
cheated. You can't take the path c , because it doesn't correctly represent the forward motion and the
sideways motion we just talked about. Obviously, the path a
represents the forward motion and the path b represents the sideways motion. Therefore, no matter how tiny you make that triangle, you have to keep the a and b paths
You will say, “C'mon, that can't be right! I can draw that triangle on the ground, and I can always walk
that c -path. There is nothing stopping me.” True, but if you are walking that
c -path, you aren't walking a curve, are you? You are walking a straight line. And if you combine a lot of those
c -paths to try to create a circle, you aren't really creating a circle. You are creating a polygon. Even if you make your circle out of thousands of those c -paths, in each little triangle you are still cutting the corner. If you cut
the corner, you aren't representing forward motion and sideways motion at the same time in your fake
circle. So it isn't really a circle. You are not creating real circular motion
. You will say, “Even so, if I make those c -paths tiny enough, I will still get the right number for the
circumference of the circle. Everyone knows that.” In this case, what everyone “knows” is wrong. In
fact, if you cut all the corners in each little triangle, you end up getting a number for the circumference
that is way too small. It is 21% too small, which is a lot. It isn't a marginal error, it is huge miss.
Newton’s provides the diagram below, where AB is the chord, AD is the tangent and ACB is the arc. He tells us that if we let B approach A, the angle BAD must ultimately vanish. In modern language, he is telling us that the angle goes to zero at the limit.
Zyxzevn wrote. This Pi does not change whatever maths or tricks you do with it.
The ball in the circle simply goes to the outside edge of the track,
making its path longer.
And it slows down a bit. It must so, because
the change in direction causes the rotation to be different from
the track's direction.
Zyxzevn wrote. But we can tweek it by changing the length of the circular track.
By making it smaller we can make Pi seem to be 2, or by making
it longer we can make Pi seem to be 4.
LongtimeAirman wrote:.
Airman. The ball in the circular loop does move slower than the ball in the straight section. Your guess about a possible rotation slowing the circular path ball is interesting. The important thing is that your idea is verifiable
Zyxzevn Wrote:
The speed of the ball is very important in the experiment.
In the video it seems to slow down quite a bit in the curved path.
It does not seem able to go a second turn, while the straight ball has almost no loss of speed.
I'm glad to help.
The static physical length of a curve based on standard Pi does not equal the distance traveled by an object moving along that curve.
We can therefore ignore drag as a factor.
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