Temporal Divergence Meter

You are being obstinate again.

The length of the hypotenuse changes as if there is an acceleration between the object and the previous center of rotation. The math says so. I got Pythagoras backing me up. Who you got?
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You don't have Pythagoras backing you up, because you are misappropriating his equation (one based on static geometry) towards a problem of dynamics. The equation of Pythagoras applies to an AREA (hence the squared terms) not a linear distance. There are only two things causing the length of the hypotenuse to change with each successive point:
1) The x-distance is changing at a constant rate (by what I have shown above, this is NOT causing any acceleration at all).

2) The AREA of the triangles increasing because of the constant Y distance and the changing X distance.

You only think there is an acceleration because you are being confused by item #2. This is because you are misapplying a formula based on area, and your mistaken acceleration is a remnant of the increasing area of the triangles. And this error of yours should show you why treating vectors by breaking them down into their orthogonal components is such an important technique to getting the proper answer.

A) There is no velocity, and hence can be no acceleration, in the Y direction.

B) There is only a constant velocity, and therefore no acceleration, in the X direction.

C) Since this is a planar motion problem these are the only two dimensions in which motion can take place in this problem. Hence there is NO sign of any acceleration.

Oddly enough, your formula is more akin to Kepler's Law (which speaks to a constant area swept of a body orbiting another on an elliptical path) than it does to rectilinear kinematics.

Are you willing to admit your error yet?

RMT

 
Are you willing to admit your error yet?
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Not a chance for that happening. You can squiggle and squirm all you want. I don't care. I guess it's just in your nature.
In fact I would ask you to independently calculate the values for the hypotenuse yourself. Each successive value increases at a changing rate. That's a fact that I can not deny. And I'm not quite understanding why you refuse to accept this fact. The hypotenuse acceleration is along the same direction that the centrifugal force was on. Making it identical in behavior to gravity. The only difference is the direction of the force or acceleration is away from the center instead of toward the center as it is with gravity.You may recall quite a while ago I introduced the idea of negative rotation being responsible for gravity. That would be an equal but opposite force to inertial force. So it's really quite easy to extend this odd little mathematical jewel into a more understandable explanation of gravity.

Is this the mysterious acceleration causing the universe to accelerate its expansion? Right under our nose all the time.

 
(sigh) Have it your way...I will just continue to shame you with facts. Actually, you will just shame yourself by ignoring the facts that I present.

In fact I would ask you to independently calculate the values for the hypotenuse yourself. Each successive value increases at a changing rate. That's a fact that I can not deny.
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I am not questioning your calculations. They are correct. It is not that math that is wrong, it is your interpretation of what they are telling you that is wrong. I have explained (but perhaps you did not understand) that the changing rate is due to Pythagorean Theorem being based on the AREA of a triangle.

And I'm not quite understanding why you refuse to accept this fact.
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Fundamentally, it is because the object you are trying to calculate the velocity and acceleration for (the mass) DID NOT TRAVEL ALONG THE LINES OF THOSE HYPOTENUSES. Kinematics of an object are based on the path the object traveled, and velocity and acceleration are time derivatives of that path. Your use of the hypotenuses is an incorrect method to calculate the acceleration of the object. Understand this: The hypotenuses do NOT describe the path of the object, hence they have nothing to say about the acceleration of the object.

The hypotenuse acceleration is along the same direction that the centrifugal force was on.
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No it is not, because that force is no longer present. The force was imparted by the string. Once the string was cut, that force (which induced the curved path) ceased to act on the body. So the last time that force was present it was NOT AT ALL acting along any one of your hypotenuses. It was acting at a 90 degree angle to the tangent path that the mass ended up following.
Again....Your analysis is wrong and you should feel shame that you are not seeking to understand why what I am telling you is the actual truth (and the math backs me, not you).

Making it identical in behavior to gravity.
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Wrong again. I will not even address any of the rest of your fallacious discussion beyond this statement of yours above. Because it is all conjecture based upon incorrect analysis, just like the analysis you gave above is incorrect. You are not doing vector dynamics correctly. Your refusal to understand how to do it correctly, and thus not admit your error, is what holds you back. But of course that same refusal is what feeds your belief that you have discovered some truth that no one else did. But it is not a truth. It is delusion, and nothing more.
RMT

 
Did I do something wrong? If I'm not mistaken, it does appear you are in denial. LOL... It's too late Rainman. You're infected with the truth. Does it hurt?

And you're trying to shame me! LOL...

 
You like to conveniently ignore the factual points I make that destroy your ignorant analysis. But I will not let you continue to get away with that. I want you to either disagree or agree with these two facts about the "analysis" you have offered. And if you disagree, explain why and cite references:

A) There is no velocity, and hence can be no acceleration, in the Y direction.

B) There is only a constant velocity, and therefore no acceleration, in the X direction.

These are facts, according to how YOU drew the diagram. And these facts can do nothing but falsify your belief (unproven) that the mass is accelerating.

RMT

 
Did I do something wrong?
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Yes, you did, and I pointed it out. You just refuse to accept it. You incorrectly assumed that the mass traveled the path of the hypotenuses, when it did not. You analyzed the wrong thing. And you did not separate your x axis motion from your y axis motion. It is a sophomoric error which yields points lost on many undergrad kinematics exams. So you are less intelligent than those students, because at least those students learn from their mistakes.

RMT

 
Fortunately, there are several different ways to explain to (willing) students how their analytic work is in error. This case is no exception. Another way to explain your error is that you are not using a consistent reference frame. You are mixing two reference frames with your hypotenuse calculations.

You introduce an X-Y grid via the means you set up the problem with an X-Y axis and constraining the motion to be zero along the Y axis and non-zero along the X axis. But then, you start to perform your analytic calculations in a completely different reference frame that is an "r-theta" (radius and angle) frame.

The most important rule of kinematics is: "Pick a reference frame and ensure all your calculations remain in that same reference frame." By calculating the hypotenuse, you are invoking the radial distance from the origin to the mass. That radius distance includes both X and Y measurements, wherease the X-Y axis system you used to setup the problem only contains motion in one of those two axes.

Once again, you give a good example of erroneous calculations that I can send my students to read to understand how they might commit errors, and hopefully avoid them. Classic mixing of reference frames. You fail Kinematics 101, Einstein.

RMT

 
A. True

B. True

How convenient that your facts actually support mine.

But then your facts reference the inertial force and its ensuing direction. And my facts reference the centrifugal force and its ensuing direction.

Now I understand that I am challenging your religious beliefs. So naturally you are opposed. And you haven't really provided a valid argument on why I can't use real math to describe something that really happens. I mean if the math works, and it fits reality, it should be good to go.

Obviously I can see that you don't like what I did. Too late. It's done.

I'm off to bed. See you tomorrow.

 
A. TrueB. TrueHow convenient that your facts actually support mine.
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But actually, they do not. If you agree to the above, then there CAN BE NO ACCELERATION in either of the two directions.

And my facts reference the centrifugal force and its ensuing direction.
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There is none. Anything "centrifugal" ceased to exist when the string was cut. Done. Over. Too late.

And you haven't really provided a valid argument on why I can't use real math to describe something that really happens. I mean if the math works, and it fits reality, it should be good to go.
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And that is the problem. The math is correct, but does not work for the situation. Math is nothing devoid of context. And you are applying the wrong math to this context.
RMT

 
You are right about one thing. It's too late to undo my exposing you to the truth. You can say there is no acceleration all you want. The math says otherwise.

You know this reminds me of a similar situation I remember when I was just a boy. Maybe 5 or 6 years old. It was just shortly after Christmas. There were several of us out playing, and a little girl had come over to join us. She was only 3 years old. We decided to tell her the truth about Santa Claus. She was devastated. Her happy little smile slowly changed to one of sadness. Then she started to pout. Which eventually led to tears. I can still see her rubbing the tears out of her eyes with her little hands. Then she got angry. She started to yell at us. She said her mother told her Santa Claus was real. Then she ran away. She didn't take the truth very well at all.

Kind of like you Rainman. Do you have a childhood memory of when you found out about Santa Claus? How long did you stay angry? Eventually you had to come to the realization that Santa was all a lie.

You're a grown man now. Eventually you'll come around and accept the reality of the math.

 
You are right about one thing. It's too late to undo my exposing you to the truth. You can say there is no acceleration all you want. The math says otherwise.(snip)
You're a grown man now. Eventually you'll come around and accept the reality of the math.
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None of your gyrations or insults of me change the fact that your analysis is incorrect. The math does NOT show there is an acceleration, because your application of that math is in error with the facts. The fact is that the mass did NOT travel the path of those hypotenuses, did it? Of course, you will conveniently ignore this because it is the basis of you being wrong. But the derivative of an object can only be properly calculated by deriving along the path the object traveled. You are taking the derivative along paths (hypotenuses) which the mass did NOT travel. Hence, you are quite wrong. Stating that you are right and I am wrong does not change that. But I realize it makes your ego feel good. You still look like a fool.
I can bring professor after professor of engineering and mathematics to this board to tell you that you are wrong...and you will still not accept it. If that is not stubbornness, I don't know what is.

RMT

 
You are correct. It's a weightless acceleration. Just like gravity. So there can be no mass.
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There is no acceleration. You are not accounting for a deceleration. It is all because your coordinate system accounting is atrocious. Soon, very soon, you will be faced with math that proves you wrong. But yes, I know, you will ignore it.

RMT

 
You are correct. It's a weightless acceleration. Just like gravity. So there can be no mass.
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And in your typical misdirection manner, this does NOT answer the question I asked. Please answer the question I asked.

RMT

 
Here is the math you are missing that allows you to come to the erroneous conclusion that there is an acceleration present:

As I mentioned to you, your accounting for TOTAL motion in both dimensions of a 2-D coordinate system is pretty bad. Your error of omission stems from, as I stated earlier, you are treating the problem as an R-theta circular coordinate system when you compute the hypotenuse. The hypotenuse does, indeed, compute the "R" (radial) component of the motion in the R-theta coordinate system. But what you forgot to account for is the "theta" (angular) component of the motion.

If you do the trig, you will come to find that the angle your beloved hypotenuse makes with the X-axis is growing smaller and smaller as the mass moves away from the Y-axis. You can even see this must be as you take the limit as the mass moves off to +infinity on the X axis. No matter how far the mass moves to the right, the angle of the hypotenuse with the X-axis will never equal zero degrees. It is an asymptote.

To prove it to you beyond a shadow of a doubt, I give you the hypotenuse values that you calculated and listed on your diagram in the first column below. In the second column below, I have computed the angle that this hypotenuse makes with the X-axis, in degrees. You will note that the angle is getting smaller and smaller with each step, and thus this acts in contradiction to the hypotenuse values getting larger.

Step # | Hypot Length | Hypot Angle to X axis (DEG) | Change in Angle (DEG)

1 | 10.04 | 84.28 | 5.72

2 | 10.198 | 78.69 | 5.59

3 | 10.44 | 73.30 | 5.39

4 | 10.77 | 68.20 | 5.10

5 | 11.18 | 63.43 | 4.76

6 | 11.66 | 59.03 | 4.40

7 | 12.206 | 55.01 | 4.02

8 | 12.806 | 51.34 | 3.67

9 | 13.45 | 48.00 | 3.34

10 | 14.14 | 44.99 | 3.01

11 | 14.866 | 42.27 | 2.72

12 | 15.62 | 39.80 | 2.47

I have even made it easier for you to see by including the last column which shows you how the change in angle gets smaller and smaller as the hypotenuse gets longer. Hence, the angle measure is decelerating while the hypotenuse measure is accelerating. If you take the vector sum (using radians for the angles) you will see that the total vector magnitude is not changing, hence no acceleration.

So there it is. As your snide remarks say "the math doesn't lie." You were just incomplete with your math. I have now shown the complete calculation in the R-theta coordinate system (which YOU chose). So what excuse will you dream up now?

Checkmate. Game, Set, Match.

RMT

 
You want to use the theory of mass to dispel the observable facts. Sorry, facts trump theory every time.
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Just like the facts I just exposed to you. OH NOES! How can you ever go back to your ignorance now that I have exposed you to math done correctly?

And no, I am not using any "theory of mass." I am using nothing but proper kinematics and calculus and trig. That is all.

You're quite the fool.

RMT

 
No matter how much you snivel, there is nothing that you can say that will dispel the computations.

I know the angle gets smaller. And I know the hypotenuse keeps changing at a changing rate. But there is something that you left out. Probably deliberately. Where are your time calculations?

 
No matter how much you snivel, there is nothing that you can say that will dispel the computations.
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Sorry pal. I just did.

I know the angle gets smaller. And I know the hypotenuse keeps changing at a changing rate. But there is something that you left out. Probably deliberately. Where are your time calculations?
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They are unnecessary. But then again, I must ask "where are yours?" I am tired of doing your homework for you.
RMT

 
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