A power generation plant converts chemical (or nuclear) energy into electrical energy. This energy is then sent out via conductive transmission line.
What would be a simple schematic for this process?
That is, if we liken it to a battery, then the positive pole would be the high voltage...
For a constant velocity the transformation seems quite simple.
Mathematically, the relation between the velocity in the two frames is:
v_inertial = v_rot + w x r
where "x" is the cross product operator and w the angular momentum vector.
Basically, v_rot is determined and then transformed...
In this case the velocity of the moving frame, v, would be the instantaneous tangential velocity, w*R, of the rotating frame at the initial coordinates at t=0.
Is that correct?
This response is just an aside, but I am using wxmaxima to do the calculations so there should be no algebra errors:
https://wxmaxima-developers.github.io/wxmaxima
Computer algebra systems eliminate those all too common pencil-pushing errors and the blame can then only be placed on the...
I think the problem I was having is that intuitively it seemed to me that the INITIAL velocity components, at the t=0 instant, should be same in both frames.
In this case, the particle is shot from the rotating disc. But the same situation would occur if the particle were shot from the...
Unfortunately, the web pages which I cited do not properly load MathJax.
For those who may be interested, I will attach a PDF file of the same web site.
OK. The velocity components are not the same in both frames.
After finding some more advanced descriptions on the web I am beginning to see the reason more clearly.
But the method I described is also NOT correct because it assumes that the velocity components are the same.
I started all...
Consider a rotating disk with the center at the origin of a stationary Cartesian coordinate system, (x, y).
At t = 0, on the circumference of the disk, someone/something shoots a particle with constant velocity components Dvx, Dvy (where the D indicates the rotating disk). Also at time t=0...
I was able to discover the solution. For one curve to roll upon another "without slipping" the arc lengths must be equal.
The arc length of the parabola, parameterized as above, is:
asinh(2*A*t)/(4*A)+(t*sqrt(4*A^2*t^2+1))/2
We need to now parameterize the circle a bit differently with a...
I am trying to develop an equation or algorithm to determine the roulette curve that results from rolling a curve over another fixed curve.
A general method to determine the roulette using any two curves, rolling and fixed, seems to be presented here...
NASA has proposed a mission to Alpha Centuri:
https://en.wikipedia.org/wiki/2069_Alpha_Centauri_mission
This mission would involve a spacecraft traveling at 10% of light speed and therefore relativistic effects could be somewhat significant.
Let's assume this spacecraft is carrying a...
A lot of scrap steel is recycled to make new steel. But how is this scrap steel refined?
Recycled scrap must be a mixture of various types of steel with each type containing different amounts of manganese, vanadium, chromium, etc. How are these other metals separated from the scrap melt so...
I understand that the evidence for dark matter, although indirect, is quite strong. Yet there are a few things that puzzle me about the dark matter idea.
If dark matter is the predominant form of matter in the universe, why does it have no effect on solar system dynamics? The solar system is...
I don't want to become bogged down in a discussion on the philosophy of science which could lead anywhere without providing much benefit.
Your energy meter is actually measuring motion. The "internal" energy of a substance is again only a statistically averaged motion.
My original question...
I appreciate the answer about the frame dependence of force and energy and I also understand that mathematics is central to any description of reality.
But perhaps "fundamental" is the wrong term to use. A better term would be "observable." We do not require mathematics to observe and...