How does wind affect a turn for an aircraft?
First, I understand how wind effects aircraft tracking. I can do the calculations involving wind correction angles, effects on ground speed, headwind or tailwind calculations, etc. I teach it in a...
View ArticleAre equations of motion invariant under gauge transformations?
We know that all actions are invariant under their gauge transformations. Are the equations of motion also invariant under the gauge transformations? If yes, can you show a mathematical proof (instead...
View ArticleNeil DeGrasse Tyson on "sharing water" with historical figures
Hello, I've heard versions of these statements (below) from other scientists, but I've never seen anyone break them down. Do molecules in air really move (diffuse?) their way around the entire globe,...
View ArticleHow long does it take to reach harmful CO2 levels in a room?
• I exhale 1 kg of CO2 per 24 hours = 41.67g/h (average) • Co2 indoors after ventilation = outdoors = 400 ppm (world average) • Co2 indoors threshold = 1000 ppm (cognitive effect) • Room volume = 32.5...
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Forces on rotating disk object
Forces on rotating disk object Hi. Is it convenient to ask following question. Suppose we have solid circular object and 5 different moments like in the picture: In moment 1 we apply force (downwars...
View ArticleMass dropped onto rotating disk
Picture a flat disk of radius r with a radial vane. The disk is rotating at angular velocity w. Assume the vane is straight, starts at the center and ends at the perimeter of the disk. A very small...
View ArticleRolling Motion direction of Velocity center of mass
Hi I have come across something confusing in rolling motion. If an object moves with a positive V_cm meaning to the right its angular velocity will be clockwise or negative. The formula is V_cm=wR but...
View ArticleVirial theorem and translational invariance
According to the virial theorem, $$\left\langle T\right\rangle =-{\frac {1}{2}}\,\sum _{k=1}^{N}{\bigl \langle }\mathbf {F} _{k}\cdot \mathbf {r} _{k}{\bigr \rangle }$$ where ##N## is the number of...
View Articlev=ds/dt, a=dv/dt: vdv=ads
In an introductory dynamics textbook, we often see this progression v = ds/dt ---> dt = ds/v a = dv/dt ---> dt = dv/a Equating the dt, we get: vdv=ads Now my question On the one hand, this works...
View ArticleMeasurement uncertainty due to thermal noise
I have a charged particle in a Penning trap. The particle motion is non-relativistic and the energy is high enough such that we can assume it is not in the quantum regime. For the purpose of the...
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Vector calculus: line element dr in cylindrical coordinates
We were taught that in cylindrical coodrinates, the position vector can be expressed as And then we can write the line element by differentiating to get . We can then use this to do a line integral...
View ArticleEqualizing airflow through multi-hole orifices
I know the Bernoulli equation for calculating the air velocity through a pressurized hole, but I am wondering if one hole of a given area behaves the same as multiple holes with the same total area....
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How is it possible for two waves to be in phase when they have different...
May I know how is it possible for two waves to be in phase when they have different amplitude? I couldn't find any existing graphs that clearly shows how the two waves are in phase, would anyone be...
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What is meant by "upper limit of work done on Earth"?
I think that the work is meant to be work done for instance in power stations. Or is it similar to work I do on a body when I lift it for example? But how can we then do that work on our Earth? I just...
View ArticleHelp with Euler Lagrange equations: neighboring curves of the extremum
I tried writing this out but I think there is a bug or something as its not always displaying the latex, so sorry for the image. I have gone through various sources and it seems that the reason for u...
View ArticleWhy is gravitational force directly proportional to the product of masses?
why is that the gravitational force proportional to product of masses why not sum of masses or something else .........
View ArticleHow do I calculate the drop force on a cord and eye bolt?
i have a question. I have set up an expierment and need some values. I have a round, 3d printed disk, 0.25 inches thick and 4 inches in diameter. In the center, i have a eye-bolt attached. I have...
View ArticleWhy does ##u## need to be small to represent the Taylor expansion
Necessary condition for a curve to provide a weak extremum. Let ##x(t)## be the extremum curve. Let ##x=x(t,u) = x(t) + u\eta(t)## be the curve with variation in the neighbourhood of...
View ArticleTrig functions and the gyroscope
Good Morning As I continue to study the gyroscope with Tait-Bryan angles or Euler angles, and work out relationships to develop steady precession, I notice that the trig functions cancel. I stumble on...
View ArticleSurface area and length (percent increase relationship)
Hi all, While calculating the surface area for an object, I was told the below statement. However, I am not sure is this correct, please can someone help me to explain this with an example? Is the...
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