Einstein
Temporal Engineer
- Messages
- 5,413
I think this is from about ten years ago when I did this. But the plot appears to be an acceleration curve. Took me a while to find it on my hard drive. I used the Pythagorean Theorem to calculate the values of the increasing radius of the weight as it moves away at right angles from its disconnect spot.
FileSnack | Easy file sharing
FileSnack | Easy file sharing
You mentioned aboce that the bucket appears to be decelerating, but the time value is on the wrong axis. The bucket is actually accelerating away from the centre point.
Between 1 and 2 seconds, the bucket travels approx. 0.1 units. (Seperation of 1 on the vertical axis, time, and 0.1 on the horizontal axis, length)
Between 2 and 3 seconds, the bucket travels approx 0.3 units.
Between 9 and 10 seconds, the bucket travels approx 0.75 units.
Because time is on your vertical axis, you have to invert the gradient to get the speed.
I decided to try and plot a couple of graphs in Mathematica to extend your work. In all of the graphs, time is on the horizontal axis.
The original plot: (Distances vs. time, gradient is speed)
Original plot extended to show how it the graph approaches a straight line:
If I did this right, it should show the derivative of the second graph, a.k.a the speed plot, gradient is the acceleration:
And finally, this shows the derivative of the above graph, so this is the acceleration graph:
So you're right, from the point of view of the centre of the circle, the object does seem to be accelerating away, which seems counter-intuitive, since there are no forces acting on it. I'm going to post these on a physics forum to try and get some more info in case I've missed anything blindingly obvious. (It feels like this is another "frame of reference" problem, but I can't quite get my head around it)
I might caution you to stay away from the physics forum. They don't like people that rock the boat. I tried to argue that Mass is a scalar over there. Since technically it's a ratio of two weights on a scale. The dimensionality divides out. Not according to those guys. Mass is a separate dimension altogether over there. Good luck.