Shape Definition and 613 Threads

1) What is the shape of equipotential surfaces of the Liénard–Wiechert potential for a uniformly moving charge in the lab frame in the x-direction, like behind(x=-r) and in front(x=r) of the charge? Is the value the same as in the static case, Coulomb potential at x=r? 2) Is there some kind of...

Suppose the speaker has a container into which pressure is pumped, a rod passes through the container with a disk strung on it with one flat side and on the other with a pointed side, will the disk move in any direction under the influence of pressure?

i started to think to maybe do an integral to find the minimum area, and then I thought that the area itself is not sufficient because there is more material depending on the slope. so I thought to do an integral depending on the length instead of x. ##dh^{2}=dx^{2}+dy^{2}## ##\int{}f(x)dh=...

Looking out the window on recent flights I have given some thought to the implications of the fact the bodies of water we see are never actually flat, anywhere, at any size. The earth beneath the bodies of water on its surface takes on the shape of a sphere of course, and one could say that...

When looking at depictions of black holes, we often get illustrations of a two-dimensional space-time where everything spirals into a "hole". The hole then leads to a singularity usually depicted as a funnel shape. Then there are images of black holes shown as spherical with glowing rings...

If big bang existed, than universe must be sphere, because explosion expand in all direction.. I read that universe is maybe flat so how this is possible? Why can we with telescope determine shape of universe?

Based on info found in this forum, I have compiled info along with personal thoughts and observations in attempt to understand the fourth dimension better any input or corrections would be helpful, along with links to sites you have found helpful in your experience. Thanks! My notes...

Hi. I remember having learnt in school that if you'd like to verify that bodies of different mass accelerate the same in free fall, but don't have a vacuum available, the bodies should be of same size and shape (e.g. spheres). This made sense to me back then because drag should be the same...

For a shape to qualify as a polygon does it have to be closed. I was just introduced to frequency polygons and was surprised to see each one was a shape that wasn't closed. The definitions of polygon that I've come across go something like, a closed shape consisting of three or more lines.

In a magnifying glass, the lenses are always circular. I don't understand why because no matter what shape the lense is, it doesn't deny its physical properties and refraction would still occur, so why are they so consistent on making circular lenses. I predicted that circular lenses may be...

Assume that players A and B play a match where the probability that A will win each point is p, for B its 1-p and a player wins when he reach 11 points by a margin of >= 2The outcome of the match is specified by $$P(y|p, A_{wins})$$ If we know that A wins, his score is specified by B's score; he...

A tile shape has been identified that can tile a surface aperiodically. Phys Org article

Would a leaf blower see a different load (in terms of back pressure and flow) depending on whether the outlet tube ends in, say a 1" nozzle, versus a flared out horn of 6" diameter? I am not thinking of viscosity effects here, but rather of Bernoulli type considerations. In the case of the...

1.Does the Maxwell Boltzmann distribution change depending on the shape of the container? Pressure and the volume is constant. How is the Distribution affected whether the gas is in: a,sphere b,cube c,cuboid? Why does/doesn’t the distribution change depending on the shape of the container...

What is ideal rear roofline(rear window and trunk) angle and shape(straight line, curve ..etc) for lower drag? Keep in mind if you increase angle, you reduce butt area / wake, but induce low pressure at rear window/trunk , if you decrease angle you increase butt/wake but increase pressure at...

I have a shape based on the idea of having a string, a closed loop, that is sitting outside a rectangle. The string is d longer than the circumference of the rectangle. I noted the sides as a and b. The shapes is formed by drawing a line around the rectangle with the string as a constraint of...

I have done all of the questions apart from c and d. For a I got the answer 2.58*10^_5 cm^3 B) 3.72*10^-7 cm But for c I don’t really know how to start. I first thought of using the formula for volume of cuboid but don’t know how that’d give the answer for the dimension. For D, I turned the...

Developers of Shape Dynamics (as Julian Barbour and Tim Koslowski) claim that Shape Dynamics will offer in most cases the same predictions as GR, and implicitly as SR. How can this possibly be true, since they get rid of time altogether and thus of any notion of simultaneity? How would they get...

Shape Dynamics implements nicely Mach's principles. But how well does it fare when it comes to Quantum Mechanics? How can it be experimentally distinguished from other theories?

What's the best shape function/element in finite element methods for phase field simulation?

I was reading a Chemistry book when I read about the three states of matter. Everyone knows what they are, but I didn't know the simplest way to describe each of the three until I read this book. It said that a solid has a shape and a volume, a liquid has no shape but has a volume, and a gas has...

Ok for (1) I would say that the order of rotational symmetry is ##8##. Would that be correct? What about ##4##? For (2) The number of lines of symmetry is ##4##. And if one would say infinity for both (1) and (2) would that be correct?And if you consider a kite. Would the order of...

Physical objects have well defined shapes, but does energy ever create well defined shapes or can it only take shape within matter?

The first plot shows a large number of terms of Zeta(0.5 + i t) plotted end to end for t = 778948.517. The other plots are two zoomed-in regions, including one ending in a Cornu spiral. Despite all sorts of vicissitudes, the plot generally spirals outwards in a "purposeful" sort of way. It is...

I am confused about the shape of the de Sitter universe. The Misner-Thorne-Wheeler says it can be regarded as the submanifold given by ##-x_1^2 + x_2^2 + x_3^2 +x_4^2 + x_5^2 = k## of a flat space with lineelement ##\mbox{d}s^2 = -\mbox{d}x_1^2 + \mbox{d}x_2^2 + \mbox{d}x_3^2 +\mbox{d}x_4^2 +...

How would you go about calculating the work done in morphing a square current-carrying loop into a circular current-carrying loop, without change in length while maintaining the same angular orientation with an external magnetic field. My book suggests defining P(potential energy) = M.B (dot...

I'm trying to see if I can calculate the peak draw weight of my bow based on the draw length and the velocity of the arrow and a known shape of a curve, but I'm not quite sure how to make such a function, if there even is such a way. This is the shape of the draw weight plotted against...

Molecular potential energy of hydrogen in dependence with atomic distance for bonding orbital is given by picture below. We can see that at large distances force between atoms is attractive and potential energy drops to minimum which corresponds to bond energy and length. This part of the...

disclaimer: this is a made up question, so I don't know if there's a valid solution possible here First let's talk about the square post, it is clear that the shot will go in only if the ball hits the side AB of the square shown below, so the probability of a shot going in is simply ##\frac 1...

Optical photon is produced e.g. during deexcitation of atom, carrying energy, momentum and angular momentum difference. So how is this energy distributed in space - what is the shape and size of single photon? Looking for literature, I have found started by Geoffrey Hunter, here is one of...

I know that phasors of a single-slit diffraction form a closed polygon or circle, but how could we infer the shape when phasors generated by slits of a multiple-slit barrier?

Hi, 2 part question trying to get tetrahedron Finite Element shape functions working: 1) How do I properly setup the shape coefficient matrix and 2) How do I build the coefficient quantities in the shape functions properly? ANY tips or corrections may unblock me and would be of much value...

I know the torque will be zero when the deflection is zero and will be maximum when the angular displacement is θ0 but how to determine the exact shape of the graph? Thanks

Gravity, inertia, conservation of momentum and angular momentum are some of the forces and conserved quantities that I could think of which will tend to maintain the shape of the Milky Way. How is the separation of the spiral arms maintained?

What is best theoretical shape of undertray for maximum downforce , maybe wing shape or venturi shape? classic "venturi shape" with diffuser "wing shape"

Hi everyone. My high-school student got the following homework exercise at school which I have problem with: Smoke from the steam locomotive is carried by horizontally blowing wind. Shape of the smoke trail is shown in the attached figure. Using the drawing, determine velocity of the wind...

Hello! What is the reason why the exclusion plots of WIMP experiments have that "U" like shape? And what sets the minimum of the curve? Thank you!

Consider the Hubble horizon as the proper distance over which Hubble expansion equals c, so that you are in the center of a Hubble sphere with a radius of about 13.5 billion light-years. As you approach light speed in any direction, does the Hubble horizon draw closer in that direction due to...

In another words, to discard the Big Crunch, we discard the spherical universe hypothesis too? k>0 able us to find a solution for a dot = 0

There used to be sold a style bicycle handlebar bags that used what I think is a formed spring steel rod that fit over the handlebars and looped under the handlebar stem that supported a handlebar bag. For whatever reason this style does not appear to be available any more. I think it is a...

My thought process was to get the mass moment of inertia of the rectangle and then subtract the mass moment of inertia of the quartercircle from it. The MMoI of the rectangle is: (1/3)(0.005*7850*.6*.3)(.3^2)= 0.212 meters The MMoI of the quartercircle is: (1/4)(0.005*7850*¼π 0.3^2)(.3^2) + ? My...

" For the conical vessel, we note that pressure is a local force, and so must be independent of conditions far away. Hence altering the shape of the flasks walls while keeping local conditions constant will not change the pressure locally, and so F = (ρgh+Pa)πr2 also holds for this flask " Can...

I have this idea for LED eyes. Basically its an LED screen behind a half spherical shape. I want the user only to see what's on the display if they are looking directly at it. So for that I would need to polarize the half sphere. The half sphere can be made out of anything, the problem is how do...

Oritals, other than s-orbitals, don't have spherical symmetry while the atomic Hamiltonian does have spherical symmetry. How is this possible?

We all know that a convergent nozzle can increase the velocity of a fluid at the throat/exit than the inlet. But there are different type of nozzles available in market now like parabolic nozzles, straight nozzles and elongated nozzles. I want to know which shape/geometry is the best to get the...

If a nucleon is let say made of 3 quarks then they rather build a triangle than a tetrahedron, so they are flat ? Why is there not 4 quarks ?

Metaphorical depictions of the universe in the shape of a 2-sphere are very common. Now, let's consider mapping the three dimensions of space onto the "surface" of a 3-sphere. Like Non-Euclidean de Sitter geometry. The surface of a sphere is positionally symmetrical. However, the positional...

I explained what I want to tell you in the picture I add. Thanks in advance.

If a person lifts weights at a particular level (by level I mean the weight amount for each exercise) and wants to keep his or her current "shape," then is there any reason that person ought to left lower levels? For example, let's say you curl 10 lbs. of dumbbells and like the figure you've...

https://www.sciencemag.org/news/2020/03/mathematics-life-and-death-how-disease-models-shape-national-shutdowns-and-other This shows how policy can be informed about differing effects of control policies in different environments. One of the bleak aspects of UK choices is shown as a graph...