Radial Definition and 481 Threads

Radial Probability Density = R(r) : Square of the Radial Wavefunction The required volume is determined by the volume of the SPHERICAL SHELL enclosed between a sphere of radius (r+dr) and a sphere of radius r rpd = radial probability density × volume of the spherical shell = R2 × 4πr2 drhow...

Homework Statement Radial component of an electric field near charge 'q'. E = (1 / 4∏ε) * (q/r^2) Need to find the potential of this which is done through integrating this and taking the negative answer, i.e. ΔV = -∫E dr This is to be along a radial path towards the charge...

Sorry for not following the template, this is a follow up to a few other old posts. In solutions to problems where a car negotiates an unbanked turn, I usually see that the centripetal force is supplied by friction. My understanding is that friction applies in the direction opposite motion...

Hey I am looking into how the position of an electron is found. I have seen a derivation for radial wavefunction http://farside.ph.utexas.edu/teaching/qmech/lectures/node79.html but this is too complex. Ideally, I would like a very simplified version of this which leads me to understand how...

Okay, this is a really basic question. I'm just learning the basics of QM now. I can't wrap my head around the idea that the radial distribution function goes to zero as r-->0 but that the probability density as at a maximum as r-->zero. How can this be? they are opposite to each other...

helo can someone tell me where I can find detailed explanation about normalization and orthogonal properties of the radial functions since the books I've been reading do not explain enough, I thought Laguerre associated polynomials resolved the problem directly but this is not the case, the...

Homework Statement Q. A metal sphere of radius 20 cm carries a positive charge of 2.0 μC. a. What is the electric field strength at a distance of 25 cm from the centre of the sphere? b. An identical metal sphere carrying a negative charge of 1.0 μC is placed next to the first sphere. There...

I found this question in a book and I am trying to answer it by myself. Here's the question and my solution. A flywheel rotates with constant angular velocity. Does a point on its rim have a tangential acceleration? A radial acceleration? Are these accelerations constant in magnitude? In...

Hi, I'm trying to locate a formula for determining the radial breathing mode of a hollow cylinder. The dimensions of the cylinder of interest are approximately .5" OD x .4" ID x .5" L Any help would be greatly appreciated. Thanks!

Homework Statement The speed of a radial-flow reaction water turbine operating under BEP conditions is 1200 rpm. The diameter of the turbine runner is 0.25 m, the inlet angle and width of the runner vanes are 125° and 70mm respectively, and the inlet guide-vane anle is 25°. The hydraulic and...

I can't figure out how to do this for the instant time or with the limited information. A particle moving clockwise in a circle of radius 2.5 m at a certain instant of a time. For that instant, find (a) the radial acceleration of the particle (b) the speed of the particle and (c) it...

Homework Statement Consider a Wavefunction: \psi(x,y,z)=K(x+y+x^2-y^2)e^{-r/a} Find expectation value of L^{2} , L_{z}^{2}, L_{x}^{2}. Homework Equations The Attempt at a Solution The first step would be a rewriting a wavefunction in terms of spherical coordinates: \psi=Kr(\cos\phi \sin...

I have a problem that I've been unable to find a simple solution for. When solving Schroedinger's equation for a central force, the nonradial part of the solution can be found with spherical harmonics, but the radial part is much more difficult. E\psi = -...

Homework Statement The density of a certain planet varies with radial distance as: ρ (r)= ρo(1- αr/Ro) where Ro= 3.98 x 106 m is the radius of the planet, ρo= 4980 kg/m3 is its central density, and α = 0.17. What is the total mass of this planet ? Calculate the weight of a one kilogram mass...

Just wondering if the two are fundamentally linked ? If the universe is in the shape of a 3 sphere and if it's radius represents time, then does the expansion rate of the radius determine what the speed of light is ? I've also read elsewhere that the passing of time is linked to the...

Homework Statement Normalization of radial Laguerre-Gauss Normalize \Psi _n (r) = h_n L_n (2\pi r^2) e^{-\pi r^2} Homework Equations \int _0 ^{\infty} e^{-x} \, x^k \, L_n ^{(k)} (x) \, L_m ^{(k)} (x) dx = \frac{(n+k)!}{n!} \delta _{m,n} The Attempt at a Solution 1 = \int...

The period of the rotation of an airplanes ellipse is T=3 milliseconds,linear speed in the top is 3*10^3 m/s.What's the centripetal(radial) acceleration of the top?I need a step by step guide it would be really helpful.Thanks.

Homework Statement In case the numbers are hard to read: Mass of the cart- .5g Initial Velocity- 1.5 m/s The height of the first hill is 2. Radius of the circle- .09m I need to find velocity (final, i think) force(s) on the cart at point A the magnitude of the force(s) at point...

Anyone know how to use the temperature gradient in a thick-walled tube to calculate the stress seen throughout the wall (radial stress gradient)? I've been scouring the internet for a good explanation but haven't found one.

Homework Statement Show that radial components of the continuum electron wave function satisfies the radial equation: {\left[\frac{-\hbar }{2m}\frac{1}{r^2}\frac{\partial }{\partial r}\left(r^2\frac{\partial }{\partial r}\right)+\frac{\hbar ^2l(l+1)}{2m r^2}-\frac{Z e^2}{r}\right]R=E R}...

Homework Statement Calculate the partial derivatives (∂f/∂x & ∂f/∂y) Homework EquationsThe Attempt at a Solution really confusing me with the use of the summation and power to 3/2. This is my attempt, most definitely wrong but still tried. ∂f/∂x = x + c1*(2*(x-x1))*([( x-x1 )^2 +...

Hi Please help me understand how charge flows in this case: There are 2 concentric cylinders, the outer one is hollow but the inner one is solid. The space between them is filled with a material of high resistivity. Now an electric circuit with voltage V is connected to the cylinder's...

Homework Statement A cell 20 microns long and 2 microns in diameter enclosed in a membrane 80 nonometers thick with a dielectric constant of 8 (neglet the ends). The cell has a potential difference between outside and inside of -70 millivolts, calculate the extra chlorine ions that must...

Homework Statement A car is traveling through a valley at a constant speed, though not a constant velocity and (I believe) it is at the bottom. If the car's speed is 25 m/s, its mass is 1200 kg and the radius of the valley (r) is 25 meters, Use your force diagram to create a Fnet=ma equation...

When a stars radial velocity is measured in search for a planet, the planet imparts a radial velocity shift proportional to m\sin i\text{ where }i is the orbital inclination of the planet with respect to our line of sight and m is the planet mass. I've heard that even though the inclinations are...

Homework Statement Im confused about something. Ill post the answer sheet to a question. It has all the data you need. BELOW: NOW... for Tangential component of the acceleration, WHY did they pick cos? and for Radial, WHY did they pick sin? I am starting to do a lot of FBD to equations...

Homework Statement The 3 kg collar B slides on the frictionless arm AA'. The arm is attached to drum D and rotates about O in a horizontal plane at the rate dθ/dt = 0.75t, where dθ/dt and t are expressed in rad/s and seconds, respectively. As the arm-drum assembly rotates, a mechanism within...

Homework Statement A horse located 8.0m from the central axis of a rotating carousel moves at a speed of 6.0 m/s. The horse is at a fixed height (it does not move up or down). What is the net force acting on a child seated on this horse? The child weight is 130N. Homework Equations...

Assuming that the accretion disk has been totally consumed by the black hole, does the temperature of the black hole due to Hawking radiation vary with respect with proximity with the black hole? For example, if I were next to the black hole, would this radiation would have a higher temperature...

I am trying to formulate an integral representing Tau between two r-values for radial motion in the Schwarzschild solution. There are a few possibilities: 1. Free fall from infinity with zero initial local velocity (v0=0 and r0 -> infinity) 2. Free fall from infinity with a given local...

The wavefunction of hydrogen is given by \psi_{nlm}(r, \theta, \phi) = R_{nl}(r)Y_{lm}(\theta, \phi) If I am only given the radial part, and asked to find the expectation value of the radial part I integrate the square of the wavefunction multiplied by r cubed allowing r to range from 0 to...

1. A Ball is in a frictionles tube that is rotating with a constant angular velocity \omega. The ball is initially held in place a distance r0 from the pivot by a string which breaks at t=0. If the radial coordinate of the ball from the origin is r(t), find r(t). I am having a very hard to...

Homework Statement In a neutral hydrogen atom, the electronic ground state 1s, and excited state 2s, are given by wave functions ψ1s = 1/π1/2 1/a3/2 e-r/a ψ2s = 1/(32π)1/2 (2-r/a)2 e-r/(2a) where "r" is the radial distance to the nucleus, and "a" is the Bohr radius. Write a C++ program...

I have attached a figure with this, to help in understanding the problem. A ring whose circumference is attached to its center by infinite springs. Center is fixed. thickness of ring is h, width is b, Young's modulus E and moment of area I. Now a radial force is applied(shown in the figure...

Having trouble calculating Radial and Tangential aspects of a cars acceleration...! Homework Statement Here, I will just post the question as an image. Never mind the one where I have to sketch, but b and c I am having trouble with. How do you calculate the radial and tangential...

Homework Statement Here, I will just post the question as an image. Never mind the one where I have to sketch, but b and c I am having trouble with. How do you calculate the radial and tangential aspects of the cars acceleration? and from that info, how do I calculate the radius...

Homework Statement A particle moves in a plane with constant radial r=4m/s. The angular velocity is constant and has magnitude \Theta=2rad/s. When the particle is 3m from the origin, find the magnitude of the velocity and the acceleration. Homework Equations The Attempt at a...

I'm trying to plot the radial probability function for a hydrogen atom. I have the function itself (Psi2*4*pi*r2) my problem is that when I plot the function with angstroms on the x-axis, the y-values are larger than they should be (they look about right if I divide them by the bohr radius in...

I'm trying to plot the radial probability function for a hydrogen atom. I have the function itself (Psi2*4*pi*r2) my problem is that when I plot the function with angstroms on the x-axis, the y-values are larger than they should be (they look about right if I divide them by the bohr radius in...

Homework Statement This shouldn't be so hard to do I guess, but I just cannot figure it out. The problem statement: Prove that the special form of the discrete Laplacian operator in radial coordinates acting on a grid function u_{l,m} at the central grid point l=0, m=0, given by...

My geometry is bit complex. I want to make a heat transfer model based on FDM in the radial direction. But it has become very difficult to discretize the domain because of multiple materials. As the segments are symmetric, I want to model the heat transfer in one segment. My schematic is given...

Homework Statement How are the number of intermediate radial nodes in a bound state wave function related to the degree of excitation? Homework Equations N/A The Attempt at a Solution Here's what I've come up with; however I think I'm missing something or perhaps not being...

Imagine you have a cylindrical plug of plastic that you press fit into a hole. I need to determine the raidal pressure, radial stress, that the plug exerts on the wall of the cylinder. Here is what I have so far. Lateral Strain = (d_initial - d_final) / d_initial\ From what I...

One of the textbooks I've stumbled across states that the radial resistance of a coaxial cable ( current running from inner cylinder to outer cylinder via silicon in between) is given byR = [resistivity * natural log of (b/a)] / [2*pi()*(length of cable)] where b is the outer radii and a is the...

Hello, I am interested in making plots similar to those attached (I have my own date :P). Any recommendations on what software to use? I suppose there are two things I would like it to do (although either one alone would be nice): 1. Create nice radial/polar diagrams with the angles and...

Homework Statement Well, I'm not sure if this is a correct subforum to post my problem, but to me it does seem to me as an academic problem. One I can not solve, apparently. Well, anyway. I'm solving the 1+1 radial wave equation using finite difference. I shifted my grid, so that the origin...

I was wondering, does anyone have any images that show the difference between the radial distribution functions for hcp and fcc lattices? I would be useful for reference purposes.

The following diagram and approach illustrates my recent thinking and revisiting on some of the calculations for the radial tidal forces and perhaps even the "force" during a flyby. Suppose we consider a series of geodesics , all flying by our massive object M, at points a, b, c,...z on a...

What do "radial bearing" and "pressure bearing" mean in physics? (This is NOT a homework question) I am told that this board is supported by two bearings: Radial bearing C, and pressure bearing O. Then they write something I can't even begin to translate, it looks as though it's written in...

Homework Statement Given the following stream function: ψ=C(sin(theta)/r) Find the radial and tangential velocity components. Homework Equations ? Don't know any The Attempt at a Solution Absolutely no idea how to even begin. Do I take the integral or something? Any help...