Shape Definition and 638 Threads

Hi folks, I'm very new to your impressive forums but just know I've come to the right place for all the pesky questions I need answers to. For starters - Does the shape\form of a stator slot in a mono-phase, squirrel cage, A\C motor really make a difference? I believe some shapes offer...

Why does H2Se have a bent shape? It has 6 valence electrons. 2 are used to bond with each of the hydrogens. 2 more up and 2 more down. So the repulsion of the lone pairs cancel off each other. Isn't this arrangement going to make the bond angle 180°?

What formula would you use to calculate the area (excluding the base)? What formula would you use to calculate the volume? What would its longest side be?

While I was doing exercises about this, I noticed that, for example f(x,y)=e^{x^2+y^2} was very similar to f(x,y)=x^2+y^2 And something similar with: f(x,y)=e^{(1-x^2-y^2)^{(1/2)}} and f(x,y)=(1-x^2-y^2)^{(1/2)} So I supposed that some transformations that preserves some properties kinda...

How certainly is the universe flat? Is is absolutely approved or not? If yes, what will cause the big crunch?

Fig 1 : the blue volume has a lot of very small spherical balls in it. Balls are under pressure from external system (weight or other), the potential energy is always the same because the blue volume is constant. When I move the blue volume from position 1 to position 2, I can understand that...

I have heard people say there is no center to the expansion of the universe. I have also heard the expansion described as an ever expanding balloon with all galaxies as dots on the surface. These to statements seem contradictorily to me. If the expansion of the universe was like the above...

If instead of a disc shaped end I have a conical end , would there be any change in the measured magnetic field strength at the end of the solenoid keeping current, core and number of turns per unit length constant ?

Hi, I'm interesting about the torque in the system like I drawn. I drawn only additional forces from curve, not the true forces from absolute pressure. The shape is full with a lot of very small circular balls (blue color). A pressure is apply from external system. The goal is to have FR...

this is not actually for homework, I am no longer in school, this is for a small application I am trying to write that compares dimensions. However, I believe this is the appropriate spot to post after reading the rules. Homework Statement okay, so let's say you got a shape, for example a...

Do you think it is possible to have a shape in the euclidean plane that has more than 2^{\aleph_0} sides. maybe some crazy fractal. and if not in the plane would we maybe have to go to infinite dimensional space.

I had read an article about a hot air balloon, when coming into balloon shape design, I had question on it. For best shape of the air balloon was the tear drop shape, but I do not know what is the physics behind it. From the article I read is about the pressure vector, and he is using an...

Homework Statement Does the size of the p orbital with the lone pair change when adding electron donating groups, such as methyl? Homework Equations N/A The Attempt at a Solution I know the electron availability increases on the nitrogen's lone pair, making it a better base, but I'm...

Hello, I would like to ask you some questions. 1) I've a closed curve (for example an ellipse, which may represent the contour of an object) represented by the set of its (known) points. I need to find the equation of that curve to pass through all and every point (exact fit). I think that...

Hi, This is my first post here. I think my question is relevant to the area of calculus hence posting here. In short: I suck at mathematics after years of trying, and I have a problem that I hope someone can help me with. Full disclosure: this is for a commercial project, so if that is not...

The event horizon of a Kerr black hole is often depicted as being spherical, but this seems to be a reference to the horizon as defined in Boyer-Lindquist coordinates, where horizons appear at a constant value of r. However, Thorne describes the "black hole's horizon bulg[ing] out at its...

Hi I have a problem where the flux of a particle beam is measured using a (nearly) perpendicular laser beam and a photomultiplier. I have a function looking like this: L(\nu) = \frac{\gamma/2}{(\nu - \nu_0 + kv)^2 +(\gamma^2/4)} I suppose this is a Lorentzian lineshape function...

Hi, I'm in the process of building a marble run out of brass wire using 15mm steel ball bearings. For ease of visualisation, it will be similar in principle to this: http://www.youtube.com/watch?v=0FRYX-kcZ9k&feature=relmfu I want to include a "jump" where the marble travels up a ramp at...

To give you a better idea, I have it drawn out here: http://tinypic.com/r/eq6ln5/6 I am calling the thickness of a rod t and the thickness of the shaft t2. I am using the basic equation Ixx = (integrate over area)(y^2)dA on different sections and then adding them all together, following the...

Hi all, I am trying to understand geometric flows, and in particular the Ricci flow. I understand how to calculate the metric tensor from the parametrization of a surface, but I am facing a problems in the concept phase. A metric tensor's purpose is to provide a coordinate invariant...

Homework Statement A block with a mass of 25 kg is hung midway between two pulleys, with a rope connecting a hook at the top of the block to each of the two pulleys. On the other side of the pulleys, both ropes are connected to blocks with masses of 15 kg. The 25 kg mass in the middle sags...

Homework Statement A block with a mass of 25 kg is hung midway between two pulleys, with a rope connecting a hook at the top of the block to each of the two pulleys. On the other side of the pulleys, both ropes are connected to blocks with masses of 15 kg. The 25 kg mass in the middle sags...

Hello: I would like to understand how to compute the shape operator (and eigenvalues etc) for a complex example like the Schwarzschild spacetime. It's easy for a submanifold in Euclidean space, but I don't know how to do it for the more advanced examples like the schwarzschild spacetime in...

Homework Statement A recent summary for the distribution of cigarette taxes (in cents) among the 50 states and Washington, D.C. in the United States reported mean = 73 and standard deviation = 48. Based on these values, do you think that this distribution us bell-shaped? Justify your answer...

A 180 degree circular arc (i.e. a half sphere) is obvious: When you rotate this about its two end points, you get a sphere. What about for something less than 180 degrees (e.g. 90)?: I believe this forms an ellipsoid, with coefficients a and b being equal, with respect to...

Hi: When a mass is accelerated, what happens to its length and volume? I know that when the acceleration ends, its length is governed by the equation l = l0 x sqrt (1 - v^2/C^2), but what about during the acceleration?

Hi Everyone, Imagine a tube of fabric stretched between two hoops, like the one's seen here.. http://www.stretchshapes.net/blog/wp-content/uploads/2012/08/A1.png That is, a cylinder made of an elastic material, under tension. Is there a name for this shape? Is there a generic equation...

In a game I'm developing, I have an ellipse which contains a blue shape inside of it like follows: http://img6.imageshack.us/img6/9518/screenshot20120815at938.png In the picture, the curves of the blue shape have the exact same arc as the area of the ellipse that it mirrors. In this...

How would you graph a square of any dimension on the cartesian coordinate system?

Hi I hope some one can help me with this one: I have a Lorentzian line profile L(√L) = 1 / ((√L - √0 )^2 + (\Gamma2/4)) for v = 0. For v \neq 0 I have \int(1 / ((√L - √0 - kvz)^2 + (\Gamma2/4)) * g(vz) dvz) I suppose the factor g(vz) dvz is a velocity factor, but how do I...

I had an idea of a planet that was spinning fast enough that at its equator, the outward force from the centripetal force would almost equate the planet's own gravity. However, this would change as you got closer and closer to the poles. I was just wondering what this planet might look like...

u = unit of distance. Take a solid cube of dimensions (1u,1u,1u) with center at (0,0,0). Cut it straight along x, y and z three times with a circle of diameter 1u parallel to the faces of the cube with the center of the circle at (x,0,0), (0,y,0), (0,0,z) respectively, removing the "shavings"...

Hello. I read from a calculus book (Larson) that shape of comet's orbit is determined by its velocity in following way. Ellipse if v < sqrt(2GM/p) Parabola if v = sqrt(2GM/p) Hyperbola if v > sqrt(2GM/p) where p is the distance between one vertex and one focus of the comet's orbit...

If the universe began from the Big Bang, then why is the universe not a spherical shape? I mean, if it expanded from a singularity, then why is it not spherical?

Howde all. With reference to matter originating from the big bang. Nothing else. No multiverse, no pbranes - nothing. Just the Big Bang. Ok - given that galaxies are moving away from each other - then there is an overall outer edge shape created by these galaxies. Lets say now that...

for a 1D free particle with initial wave function \phi(x') square shaped(e.g. \phi(x')=1,x'\in [a,b],otherwise it vanishes), my question is: how does it evolve with time t? if we deal with it in P basis, it is easily solved, using the propagator U(t)=∫|p'><p'|e^{-\frac{ip'^2...

I am a bit confuse on the back EMF waveform shape of the brushless permanent magnet machine. As I know brushless DC permanent magnet motor has a trapezoidal shape back EMF waveform. If I use this motor as a generator, do I still get the same waveform shape or I will get a sinusoidal waveform?

this is from Krauss' A Universe from Nothing: I don't understand why that is the case. I don't need a real in depth explanation just a few nuggets of information.

Homework Statement Not homework, but something I'm interested in finding out. The setup is a flexible wire with left endpoint fixed at x=0 and right endpoint at x=L. You push the right endpoint with some horizontal force directed towards the left endpoint which will move the right endpoint...

Hi all, I have a mostly theoretical question here. I have a copper rod approximately 2cm in diameter and 3cm tall. It is fit snugly inside a much taller cylinder. Heat enters through the base of the copper rod and exits through the sides into the tall cylinder. I need to improve conduction...

As we know a circle view at an angle appears as an ellipse , as you see in the picture, the center of the camera aim to the center of the circle , the angle between the circle axis and the camera is ө, the azimuth between mojor axis(a) and the camera is ∞, the rotation of the camera is €...

As we know a circle view at an angle appears as an ellipse, as you see in the picture, the center of the camera aim to the center of the circle , the angle between the circle axis and the camera is ө, the azimuth between mojor axis(a) and the camera is ∞, the rotation of the camera is €...

Let's say we have 2 different conductors - one a round wire, another a round wire but with hollow core. The wire with the hollow core has higher resistance. But for the sake of argument, let's assume that it has the same resistance and the round wire. Will the skin effect be less for the...

What's it called when a 3D shape can be made of 2D surfaces of all the same shape and dimensions? To make a cube, I can use 6 4-sided-squares (of course they're 4 sided) To make a pyramid (3 sided), I can use 4 3-sided-triangles I can do this with pentagon as well (i don't know what the...

Sometimes I get frustrated with the dialogs in this forum because there are so many misunderstandings and outright half truths being passed around (including from myself). Well, I was just over at SciForums.com warily participating in the thread “According to SR…” and it gave me a whole new...

I am looking for an equation (or method to develop the equation) for bending of an irregular shape. I have only been able to find bending equations for beams. The attached picture shows the shape of the gusset being bent and the location of the force. If this were a beam it would be a cantilever...

Homework Statement I'm trying to determine the limits for a double integral over a symmetric trapezoid or equilateral triangle. I'm not trying to determine the area, and therefore using symmetry to simplify the integration is not an option. The limits for the integration over the y-axis are...

This isn't a homework question in its entirety, I'm just wondering what the difference is between a Mode ratio and a mode shape? I'm taking a mechanical vibrations course and trying to figure out what the problem is asking for when it wants a mode shape...

which would have greater pressure at the end, an L shape or Y shaped funnel?

What topic in mathematics would something fall under if you assumed a complex shape to be a more simple shape? Such as assuming a recliner is actually a cube, or a tree it actually a cone or prism, or a tire is actually a cylinder? Would this be topology, or something else? Simple geometry?