Radial Definition and 481 Threads

Is there an experimental verification of the radial probability density for the hydrogen ground state given in the introductory texts. See the following link as an example. Thank you in advance. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydrng.html#c1

The Schwarzschild spacetime can be foliated by 2-sphere, which are spacelike hypersurfaces of constant t and r (Schwarzschild coordinates) with a normal vector ##\partial_t## (outside the horizon). Because a 2-sphere has no center, the coordinate r is not the radius of the sphere and we consider...

\oint E\cdot dA=|E|\int_{0}^{2\pi}\int_{0}^{\pi}(1+1/2sin6\theta\sin5\phi)^2sin\phi d\phi d\theta =|E|\int_{0}^{2\pi}(\frac{25}{99}sin^2(6\theta)+2) d\theta =|E|\frac{421\pi}{99}= \frac{\rho_{q}}{\varepsilon o}\int_{0}^{2\pi }\int_{0}^{\pi }\int_{0}^{(1+\frac{1}{2}sin6\theta sin5\phi...

when we need to find the direction of radial velocity should we move our right hand from the omega (angular frequency) vector to the radius vector ?or opposite ?

This is a tiny part of a presentation I am giving Friday, any and all help is appreciated. Homework Statement Suppose we have a circle centered on O. We are looking for the distribution of the points generated by the following method: We choose a random radius of the circle, and then choose...

For an axisymmetric long tube, it is said that radial displacement is independent of axial coordinate. What is the justification for this simplification?. If u, v and w are axial , tangential and radial displacements then u=u(x,θ,r) v=v(x,θ,r) w=w(x,θ,r) Where x,θ,r are polar coordinates...

Homework Statement Consider Schwarzschild spacetime. A) Show that the equation for ingoing/outgoing radial light rays is dt/dr = +-r/(r-2m) in t,r coordinates and dt*/dr = -1, dt*/dr=(r+2m)/(r-2m) in t*,r coordinates B) Sketch the local light cones in t,r and t*,r coordinates C) Explain...

I have a conveyor that travels radially. I need to calculate the HP needed to move it. It works on a concrete slab. The Motor RPM is 1750 and a reducer of 180:1. Any help would be great. Thanks

Homework Statement I'm trying to calculate delta r * delta p for the Hydrogen atom in the 2s stateHomework Equations ψ(r) = (1/ 2√π) (1 / 2a)^(3/2) (2 - (r/a)) e^(-r/2a) where a is the bohr radiusThe Attempt at a Solution I figured out that <r> = 6a, but I'm at a loss as to how to figure out...

Homework Statement A hollow metal cylinder has inner radius a, outer radius b, length L, and conductivity sigma. The current I is radially outward from the inner surface to the outer surface. Find an expression for the electric field strength inside the metal as a function of the radius r...

Mach's principle is considered falls by many because mass anisotropy would not be consistent with the Huges-Drever experiments, which showed the isotropy of nuclear resonance. However, anisotropy appears as well in GR in the form of radial length contraction, which can be interpreted as increase...

I am working with existing accelerometers attached to the shell of a simply supported cylinder. Accelerometers are oriented radially at +/- 45 degrees from horizontal. There is a forced vibration on the cylinder in the vertical and horizontal directions and the cylinder is also exposed to...

My book says (Foundations of Astrophysics): " The radial velocity ... can be found from the Doppler shift of the star's absorption lines: \nu_{r}=\frac{\Delta\lambda}{\lambda}c If the star you are observing is part of a spectroscopic binary system, you can separate the radial velocity of...

My question is more general than anything. When do I use centripetal acceleration vs. radial acceleration. The solutions in my physics book define a in polar coordinates as positive (v^2)/r. However, my professor uses -((v^2)/r). When do I know when to use each respective form? Thanks

Homework Statement One end of a cord is fixed and a small 0.500 kg object is attached to the other end, where it swings in a section of a vertical circle of radius 2.00 m as shown. (I don't have access to a camera right now, apologies.) When the angle is 20.0 degrees, the speed of the object...

I am a hobbyist and I have designed a radial turbine device for use in a tidal stream. I have conducted a couple of experiments to demonstrate that there is less mechanical stress in the radial approach as compared to the axial approach but I would like to prove this concept mathematically (at...

Homework Statement Three stock car drivers are racing around a circular bend. They are each circling the bend at different radii: r1=249 m, r2=255 m, and r3=261 m. At a given instant, all three are traveling at the same transverse rate of rotation...

Homework Statement I am trying to derive the formula a_r=\frac{v^2}{r} for uniform circular motion (for personal understanding, this is not an assignment). But am having some difficulty. I have seen other proofs, but I want to know why my approach is wrong. The Attempt at a Solution...

Homework Statement A wheel changes its angular velocity with a constant angular acceleration while rotating about a fixed axis through its center. Show that the change in the magnitude of the radial acceleration during any time interval of a point on the wheel is twice the product of the...

Hi, I am wondering why radial variation in Poisson's ratio exists when a cylinder is compressed? Ie, Poisson's ratio toward the center is lower than what is measured at the circumferential edge. Thanks M

Hi, I am reviewing a problem with the associated solution and there is something i don t understand. Imagine a triangle with vertices l, masses m are attached to the two end of the vertices and on the top end vertice there is a pivot so that the triangle can swing. We start with the triangle...

Homework Statement I got the the radial part of the Laplace-Equation: r^2(\frac{d^2}{dr^2}U(r))=l(l+1)U(r) Now I should show that the following solves the equation: a_l*r^l+\frac{b_l}{r^l} The Attempt at a Solution The problem is that I got l(l-1) instead of l(l+1) :(

This is a specific case involving a Jaguar, but any help on the correct way to find the radial axial and torque loads in a moving cars wheel would be greatly appreciated. Thanks in advance Homework Statement Estimate the worst case radial, axial and torque loads on a wheel. Mass of...

I am trying to do the problems in this set: http://farside.ph.utexas.edu/teaching/336k/lectures/node13.html They seem quite hard, but I think I've managed to get to #4. The statement of the problem is at Problem 4 in the above link. My attempted solution is the following: The...

Homework Statement I attempted this problem, and i have a midterm tommorow. I thought my approach was correct but I don't have a clue if it actually is. I drew a simple right angle triangle according to the information given in the question. A ball swings in a vertical circle at the end of a...

A particle of mass 0.014 kg is traveling on a radius 0.9m at a rotational velocity of 36+5*t rad.s-1. How many revolutions does the particle go thorugh in 4.8 seconds? [revs] What is the radial force on the particle at 4.8 seconds? [N] (Hint: consider directions) (question I'm stuck...

Homework Statement A metal sphere is attached to the end of a string and then set in motion such that it rotates in a horizontal circle as shown in the sketch. The metal sphere has a mass of 0.5kg and the radius of the circle is .2m. 1)Find the tension in the string 2)Calculate the radial...

I am (attempting to) learn the *basics* of quantum physics in terms of the origin of atomic orbitals from the Schrodinger equation. I understand that the solution for H is split into a product of 2 functions, the radial wave function and the angular wave function. Then I am being shown plots...

Homework Statement High resolution spectroscopy reveals that the H line is located at a wavelength of 656.250 nm for this star. The wavelength of H measured in the lab is 656.280 nm. Calculate the line-of-sight velocity of the star. Homework Equations Here's the Doppler...

Write the expression for the infinitesimal radial inertal force dfr "look at pic" Consider the non-uniform rigid disc of Figure 1. The density of the material is variable and depends on the radial position: p = p (r). Its analytical expression is p=po+p(1) and where Po and P(1) are known and...

Imagine you are getting dressed in the morning and fastening a belt around your waste. You pull on the loose end of the belt, developing tension T throughout the length of the belt. Using this information, how can you determine the amount of compression the belt is applying to your waste? I...

Radial Artery harvesting is becoming and more and more used as an option for bypass surgery. I have read that there is an increase in the risk of pour tissue oxygenation, which of course makes sense. You can read more in - http://lib.tmd.ac.jp/jmd/5202/01_manabe.pdf, where it is also referred...

Homework Statement Carefully study the following plot of electric field E in N/C versus distance r in m and answer the questions that follow. The electric field is directed radially outward, and the variation of E with r is independent of direction. [/b] For each statement, select "True" or...

Homework Statement A car changes speed as it turns from traveling due south to heading due east. When exactly halfway around the curve, the cars velocity is 19m/s at 45° south of east. At this moment, the cars total acceleration is 3.0 m/s2 at 20° north of east. Calculate the radial and...

Consider a light ray emanating from the origin of a FLRW coordinate system in a homogeneous, isotropic universe. The initial velocity of that ray will have only x0 (t) and x1 (r) components. In papers I have seen it is assumed that its velocity will continue to have zero circumferential...

All I need to evaluate the normalization coefficient. I need a step by step guide. It will be a great help if someone please tell me where can i get the solution (with intermediate steps). I think the solution can be done using the orthogonal properties of associated Laguerre polynomial. I need...

The radial part of the Laplacian in spherical coordinates goes as: \frac{d^2}{dr^2}\psi+\frac{2}{r}\frac{d}{dr}\psi How can this be Hermitian? The first term can be Hermitian, but the second term, with its 2/r factor, seems like it's not Hermitian?

Would it be possible to measure the radial velocity of stars with large exoplanets using amateur equipment?

Hi! I am reviewing for the Physics GRE and am perplexed by this problem: Homework Statement A ball swings in a vertical circle at the end of a rope 1.5m long. When the ball is 36.9 degrees past the lowest point on its way up, its total acceleration is (-22.5, 20.1)m/s^2. At this instant...

Hi, When can I assume that the solution the laplace equation (or poisson equation) is radial? That is, when can I look only at (in polar coordinates) \frac{\partial u^2} {\partial^2 r} + \frac{1}{r} \frac{\partial u} {\partial r} = f(r,\theta) instead of \frac{\partial u^2} {\partial^2 r}...

Homework Statement A point on a rotating turntable 20.0 cm from the center accelerates from rest to a final speed of 0.700m/s in 1.75s. (a) At t = 1.25s, find the magnitude and direction of the radial acceleration, (b) the tangential acceleration, and(c) the total acceleration of the point...

As you probably can see from the above shot, I'm determining charge density via the Laplacian over the potential (phi). I understand the mathematical steps, just confused on the factor of 4pi that pops up in the denominator. I think I understand why you would do that and here's my reasoning...

Hey I have an accelerated circular motion problem. I have only the position equation, from which I derived the velocity and acceleration. how can I tell what is the tangential acceleration and what is the radial acceleration? If you could point me towards a source to read about the...

Hi, I got a ball in a circualar motion on a frictionless table and in a uniform circle. I need to calculate the tangential acceleration and radial acceleration. What I know: Radius: 0.4m Tangential velocity: 0.50m/s^-1 (constant)Are theese formulas right for this problem? Radial...

Homework Statement Let \vec{R} = (t + \sin t) \hat{i} + (t + \cos t) \hat{j} denotes at time t the position of a moving particle. Determine the radial and circumferential components of acceleration as a function of t. Homework Equations v_r = \dot{r} v_{\theta} = r\dot{\theta}...

The Green's functions for a 3d wave are like δ(r - ct)/r -- so if you have static source at the origin that is turned on at t=0, you get an expanding ball around it of radius ct, with strength 1/r. If you look just at the XY plane, you see an expanding disc of value 1/r. Similarly, if you...

I was reading through an example question calculating the electric field in a solenoid and it made an assumption that the radial electric field must be equal to zero because there is no excess charge in the system. I don't understand when this is true or even why it is true, any suggestions...

Hi there I was wondering if someone could give me some insight on the following question. Suppose you have a radially asymmetric heat flux in the outer surface of a pipe. The inner surface is cooled. This will give you two temperature gradients; one across the pipe thickness and one along...

Hi, I'm doing a homework problem in my modern physics class and I'm stuck at a point. The question is "Show that the radial probability density of the 1s level in hydrogen has its maximum value at r = a0, where a0 is the Bohr radius" I know that the radial schrodinger equation will...

Homework Statement Here is a picture of the problem with the free body diagram: http://dl.dropbox.com/u/64325990/HW%20Pictures/problem101.PNG I am confused about why the free body diagram has the force vector in the direction of the aθ. When I did it I thought the force that the rod...