Radial Definition and 453 Threads

I am reading introductory physics from Serway. Where they say if a_r is radial acceleration and a_c is centripetal acceleration then a_c = v^2/r and a_r = -a_c = - v^2/r But aren't the radial and centripetal acceleration same (correct me if I am wrong)? Why is there a minus sign? The...

I'm in the first of 3 courses in quantum mechanics, and we just started chapter 4 of Griffiths. He goes into great detail in most of the solution of the radial equation, except for one part: translating the recursion relation into a form that matches the definition of the Laguerre polynomials...

Hello, The following has been confusing my friends and I, I want to make sure I have this clear as it is fairly elementary. (note set c = 1) Ed is falling radially into a black hole, the Schwarzschild metric is: ds2 = (1-2μ/r) dt2 - (1- 2μ/r)-1 dr2 his proper time is dτ2 = (1-2μ/r) dt2 -...

After I have an expression for the stream-function in a problem, I can differentiate to get the tangential and radial velocities because I need those to solve the problem. But I don't understand when the tangential velocity will be 0 and when the radial is 0. Can some on explain?

Homework Statement A unit sphere at the origin contains no free charge or conductors in its interior or on its boundary. It is, however, embedded in a dielectric medium. The dielectric is linear, but the permitivity varies by angle about the origin. It is constant along any radial direction...

Homework Statement We have a sphere of radius a with permanent magnetization \mathbf{M}=M\hat{e}_{\mathbf{r}}. Find the magnetic scalar potential. Homework Equations $$\Phi_M(\mathbf{x})=-\frac{1}{4\pi}\int_V \frac{\mathbf{\nabla}'\cdot\mathbf{M}(\mathbf{x}')}{|\mathbf{x}-\mathbf{x}'|}d^3...

Consider a spherical star made of N (very large number) particles interacting via gravity.Let the mass of ith particle be mi and position be xi Let ##I= \sum_{i=1}^{N}m_{i}r_{i}##, U be potential energy and K be kinetic energy 1)Show that the virial equation takes the form...

Hi, I've found geodesic equations for the metric: \begin{equation} ds^{2} = -c^{2} \alpha dt^{2} + \frac{1}{ \alpha } dr^{2} + d \omega ^{2} \end{equation} where \begin{equation} \alpha = 1 - \frac{r^{2}}{r_{s}^{2}} \end{equation} I have found that for a light ray: \begin{equation}...

Hi everyone. I'm having a relatively hard time in understanding Griffith's explanation of why the radial component of a magnetic field of a solenoid should be zero. He says, "If B(r) were positive, if we reversed the direction of the current, B(r) would be negative. But switching I is...

Radial Flow Water Pump--How to calculate Watts required to power it Hi all, I'm currently working on an independent project where I'm building a radial flow water pump to be sent to a village in Senegal. I'm having trouble figuring out what motor to use to power this water pump and how much...

Homework Statement First off, I am not a physics student. I am a math major taking a maple software course and there is a question that I can not figure out. The question gives me a radial coordinates r r:= \frac{a*t^{2}*e^{-b*t}}{1+t^{2}} And angular coordinates: θ:=b+c*t^{2/3} Where...

Homework Statement Hey Guys! Here's my problem: ψ=2(Z/a)^3/2*e^ρ/2 for the 1s orbital of a hydrogen atom. Write down the radial distribution function expression (P) of a 1s electron and determine the most likely radius. ρ=2Zr/a Z nuclear charge r radius a Bohr's radius Homework...

Hi guys, I'm doing a quantum course at the moment, and there's one thing in Binney's book which I don't really understand: Why must you multiply the radial eigenfunction by ##Y_l^m## to get the "complete wavefunction" ? They do this to normalize the eigenfunction, and to do things like...

Homework Statement The normalized energy eigenfunction of the ground state of the hydrogen atom is ##u_{100}(\underline{r}) = C \exp (-r/a_o)##, ##a_o## the Bohr radius. For this state calculate 1)##C## 2)The radial distribution function, the probability that the electron is within a...

Hi, Homework Statement I am trying to determine the magnitude of the acceleration, registered by an observer in the lab, of mass m forced to move along a radial track, immediately as it begins moving along the track. Please see attachment. ω=αt and the entire set up is horizontal. The initial...

What is the difference between "tangential and normal components" and "radial and transverse components" ? I mean in both cases, the two components are perpendicular to each other and one of the components causes the particle to rotated around, the other one gives it a speed to rotate with. Is...

Dear all, I meet a difficult question as follows: -\frac{1}{ρ^{2}}\frac{d}{dρ}(ρ^{2}\frac{dR_{l}}{dρ})+[\frac{l(l+1)}{ρ^{2}}+V(ρ)]R_{l}(ρ)=ER_{l}(ρ) (1) let x=ln(ρ) and y=ρ^{1/2}R_{l}(ρ) ,then y^{''}=γy...

Particle is traveling along a plane smooth curve.At any point an acceleration is 1 . Resultant of radial and transeverse components? 2. Resultant of tangential and normal components? Are both 1 and 2 valid?

I ma having a little bit of trouble distinguishing radial and tangential acceleration. For example: The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if: A. the magnitudes of the angular velocity and the angular acceleration are each...

I think the solution to the radial schrodinger equation includes a form of the Laguerre polynomials, the polynomial v(ρ). Does anyone know what this v(ρ) polynomial is called? The only information my book gives is: "The polynomial v(ρ) is a function well known to applied mathematicians."...

Homework Statement Determine the radial dependence of gas density for an isothermal cluster of galaxies with temperature T that has a total mass density profile given by the Navarro, Frenk, & White form: ρ(r) = ρcδc , (r/rs)(1 + r/rs)2 where ρc is the critical density, rs is a characteristic...

Greetings, all. I'm working on a real-time star map for a role-playing game where each star is located in its time-corrected 3d coordinates. With this, each star will be where it should be in a moment of time and not where it is observed to be. To do this, I take the proper motion of the...

Hello, If I have a shaft that has a section area of .0562 in. sq. and a material yield strength of 60KSI. And I will have the force applied at the top of the shaft pushing down. The shaft will be in a cantilever configuration where the force will be applied .125" from the base of the shaft...

Hi all, I want to calculate how tell if a particle in a centrifuge in deep space will move towards the rotation axis or to the rim of the fluid. There is no container walls. This is not a HW problem. I watched the video and wanted to learn more about this. (it is under the you-tube...

Hello, would someone know where could one purchase a radial inflow microturbine of diameter 1 - 2 cm All I need is a contact web address or similar of the manufacturer or seller. Many thanks

I've been reading the excellent article from Morris and Thorne: "Wormholes in spacetime and their use for interstellar travel a tool for teaching general relativity" and there's something I don't quite get it. In the ninth page the authors state: "[...] in the general case, the radial coordinate...

Homework Statement Here is the part of the problem that I am referring to (that is also fully portrayed in a more aesthetically-pleasing manner in the TheProblem.jpeg attachment).: Consider a particle moving on the curve whose equation in polar coordinates is r = 1 + cos(θ). The rate of change...

Homework Statement Hi I am trying to find the off-axis x-component of the magnetic field produced by a current-carrying coil. The on-axis case is done here, where the axial (z-) field is found and the x-component is of course 0 due to symmetry. I am pretty sure I know how to do it: I end up...

I've been playing around with some MD simulations, a field not really familiar to me. I put together a code in LAMMPS to simulate a Lennard-Jones fluid and compute the RDF. I get the oscillations one would expect, which is good, but what is surprising is that the minimum of g(r) after the first...

Homework Statement (a) A particle moves in a plane with constant radial velocity [(r)\dot] and constant angular velocity [θ\dot]. When the particle is at distance r from the origin, determine the speed of the particle. Data: [(r)\dot] = 3.2 m/s; [θ\dot] = 2.3 rad/s; r = 3.2 m. (b) When the...

In a galvanometer the magnetic poles are cut in such a fashion which ensures radial magnetic field. If field is radial then the angle between magnetic moment i.e Area vector of the coil and field is zero. Thus the coil should not experience any torque when current is passed through the coil...

Hi all, I have started with my understanding of pressure vessels and i have some queries on the topic. 1) I understand the part of axial stresses.When a cylinder capped at both ends is subjected to internal pressure,it tends to increase the length of the shell,and therefore a resistance is...

Hi guys, Heard an interview question from a friend, the guy asked him what happens to a disk with internal radius r and external R such as the following: When heated. He told me the answer is that the internal radius gets smaller and the external gets bigger. Can anyone help me understand why...

Homework Statement The problem is number three (page 3) on the following link.http://panda.unm.edu/pandaweb/graduate/prelims/QM_S12.pdf I was going to type it out but it got too messy. 2. The attempt at a solution What I want to know is the relevant unitless variable substitution that...

http://imgur.com/euMW6FO In the above question, why is coriolis acceleration in the positive eθ direction?. The system is rotating in an anti-clockwise direction, and in the er direction the velocity of the cam is radially outwards. Would this mean that the coriolis acceleration is to the...

Homework Statement A wheel with a radius of 0.2 m has a constant angular acceleration of α = 3.00 rad/s^2. Find the radial acceleration. Homework Equations a[SIZE="1"]rad = ω^2*r ω^2 = ω[SIZE="1"]o^2 + 2*α(θ - θ[SIZE="1"]o) → ω = √(2*α*θ) The Attempt at a Solution ω = √6 rad/s →...

Morning all, This is probably going to seem absurdly simple, however I need to do a very quick conduction calculation as part of a much larger problem I am working on. I was wondering if anyone would be able to give me some pointers as time is of the essence. The scenario can be simplified as...

http://www.answers.com/topic/radial-and-transverse-components From the above link, 1) e θ is a unit vector perpendicular to r in the direction of increasing θ. Where is the direction of increasing θ? Is that a circle? θ Increase from 0 to 2∏.then eθ moves in a circle? direction always...

A ball tied to the end of a string 0.50 m in length swings in a vertical circle under the influence of gravity. When the string makes an angle x= 20 degrees with the vertical, the ball has a speed of 1.5 m/s. Find the magnitude of the radial component of acceleration at this instant. So i have...

Suppose there is a radially free falling object starting at r(t=0) = r0 > rS with some initial velocity v. And suppose there is a radial light ray starting at R(t=0) = R0 > r0. Suppose that both the object and the light ray reach the singularity at the same time. Question: is there a simple...

Why is there only a radial component of acceleration present if a body is undergoing uniform circular motion whereas in non uniform circular motion both tangential and radial component of acceleration are present?

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...

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...