Radial Definition and 481 Threads

Homework Statement Are you supposed to write directions for the tangential and radial components of acceleration?Homework Equations The Attempt at a Solution Because they are components, I'd say no... isn't a component usually written without a vector sign, and therefore no direction? The...

Homework Statement When I'm trying to find the probability of finding an electron within a sphere of a certain radius, do i integrate the radial distribution probability function with respect to r from 0 to infinity? My book says the product of the radial distribution function times dr would...

Hello, I was trying to do this problem and then I looked at the solution manual and found something that confused me. I am having trouble distinguishing between centripetal and radial acceleration. According to the equation in the book a_r=-a_c, which kind of confuses me. Isn't a centripetal...

Had a problem on a test today where a constant radial velocity of a particle was given in radians/sec with parametric equations that defined a spiral. Later it asked if the particle was accelerating radially, linearly or a combination of the two and I put linearly only because I figured if the...

Homework Statement Find the domain of the function. h(x) = \sqrt{4 - x} + \sqrt{x^2 - 1} Homework Equations a2 - b2 = (a - b) (a + b) I think that's all... The Attempt at a Solution For starters, I know we can't have a negative number in the radical. I looked at the 2nd radical first and...

This is a very basic question, and not specific to one single homework assignment, but general to many similar types of problems. If an object is moving in a wheel (like a ferris wheel), I understand how to determine its radial acceleration. But if a problem simply asks for the objects...

Have a spinning rotor/impellor with open channels directed radially outward (similiar to a radial vane centrifigal pump with 90 degree straight blades - such as an older automotive heater fan ). The channels have constant area from the inner to outer radius. Realize this isn't a very efficient...

Homework Statement Hi. For the question given (attachment) where does the factor of 2PI in the function for sigma come from in the first step because I don't get it in my working for the first step. Homework Equations see attachmentThe Attempt at a Solution I got sigma (without the 2PI) by...

Sorry in advance my english, I tried to translate it to english as good as I can Homework Statement When l has its maximum value, the hydrogen atom radial equation has a simple form of R(r) = Arn-1e-r/na0, where a0 is Bohr's radius. Write the respective radial schrödinger equation. Homework...

Homework Statement The solar-like star HD209458 with a mass of 1.14 solar masses exhibits radial velocity variations with a period of 3.52 days and an amplitude of 84m/s. What is the mass of its companion and what type of object is it? Homework Equations M/m = r/R = v/V [M,R,V = star, m,r,v...

The Hydrogen Atom wave function. With the substitution u(r) = r.R(r) p=kr We get a simplified version: d^2u/dp^2 = [1 - (p_0)/p + l(l + 1)/(p^2) ].u Im sure some of you have seen that before. Now, in the limit, p goes to infinity, I understand that we get u = A.exp[-p], but in...

Homework Statement "Let F be a central vector field, that is, F(x,y,z) = h(x,y,z)(x,y,z) for some smooth function h. Prove that its potential V is radial, i.e., V(x,y,z) = g(\sqrt{x^2 + y^2 + z^2}) for some smooth function g" Homework Equations Since we know that a central vector field must...

Homework Statement The ground state (lowest energy) radial wave function for an electron bound to a proton to form a hydrogen atom is given by the 1s (n=1, l=0) wave function: R10 = (2 / a3/2) exp(-r / a) where r is the distance of the electron from the proton and a is a constant. a)...

Hey everyone, I'm starting a research project for my partial differential equations course, and I've chosen to research numerical solutions to the radial form of Schrodinger's equation. From some preliminary research, I've found information on using Numerov's method, but I am really not...

This was actually an old problem I got wrong. Homework Statement ) A skateboarder rolls down a semicircular ramp (half pipe) of radius 4.0m, starting from rest at the top of the ramp (figure 1). Assuming the surface to be frictionless, calculate his radial and tangential acceleration...

Homework Statement A car in an amusement park ride rolls without friction around the rack shown in homr1.gif. It starts from rest at point A at a height h above the bottom of the loop. Treat the car as a particle. (a) What is the minimum value of h[I] (in terms of [I]R[I]) such that the car...

Homework Statement Show that the radial function R_{31} is normalized.Homework Equations \frac{1}{a_{0}^{3/2}}\frac{4}{81\sqrt{6}}\left(6-\frac{r}{a_{0}}\right)\frac{r}{a_{0}}e^{-r/3a_{0}} \int^{\infty}_{0}r^{2}R_{31}*R_{31}dr=1 The Attempt at a Solution So I plugged that radial function in...

I'm getting two different radial equations depending on when I plug in the angular momentum piece. Here's the Lagrangian: L = \frac{1}{2} \mu (\dot{r}^2 + r^2 \dot{\phi}^2) - U(r) The Euler-Lagrange equation for phi gives angular momentum (conserved), which can be solved for \dot{\phi}...

Homework Statement Determine the most probable radius of an electron for a 2s hydrogenic atom. Homework Equations r*=a0/Z where a0 is Bohr radius The Attempt at a Solution Well, I know that the answer is ~5.2a0/Z. The book tells me that the most probable radius for hydrogen (EDIT - a 2s...

Homework Statement What is the relationship between the magnitude of a radial electric field and and its associated potential? Choose the correct general relationship? Homework Equations The following alternatives are given: a) E(r)= dV(r)/dr b) E(r)= V(r)/r c) E(r)= -dV(r)/dr d)...

Homework Statement Its a conceptual question: Theoretically, how does the radial force exerted on an object vary with the radius of its circular path when it is revolving: (a) at constant frequency? (b) with constant speed? Homework Equations F = mv^2/r The Attempt at a...

I have ~5.24a_o where a_o is the Bohr radius given by 5.291772E-11 m. This is my r value. But I am getting HUGE radial probability densities ~10^8! How is this possible? I thought they have to be less than 1 since it's a probability! P(r) = |rR(r)|^2 = [r^2 / (8a_o^3)] [(2-r/a_o)^2] exp(-r/a_o)

Homework Statement The Milky Way galaxy (including the sun) rotates about its center with a period of 200 million years. The sun is approx. 2 X 10^20m from the center of the galaxy. What is: A) The radial acceleration of the sun? B) What is the net gravitational force on the Sun due to other...

Homework Statement Calculate the probability that the electron in the ground state of a hydrogen atom is in the region 0 < r < 3.75a0. Homework Equations a0=.0529 nm P(r)=4(Z/a0)^3*r^2*e^(-2Zr/a0) The Attempt at a Solution I am confused because I am not sure if I am supposed...

I have picked up "Roark's Formulas for Stress and Strain" and "Mechanical Vibrations" and have been unable to reach resolution on a particular problem. I am interested in the behavior of a uniform cylindrical shell (cylinder diameter >> wall thickness) rigidly clamped at both ends wherein...

Homework Statement I need to find the momentum space function for the ground state of hydrogen (l=m=0, Z=n=1) Homework Equations \phi(\vec{p}) = \frac{1}{(2\pi\hbar)^{3/2}}\int e^{-i(\vec{p}\cdot\vec{r})/\hbar}\psi(\vec{r})d^3\vec{r}...

This is not homework, but is not general discussion, so not sure where this would go. In class we were deriving with the radial equations of a hydrogen atom, and in one of the equations was the commutator term: \left[ \frac{d}{d\rho}, \frac{1}{\rho}\right] my attempt was: \left[...

Homework Statement A ball swings in a vertical circle at the end of a rope 1.50 m long. When the ball is 37.5° past the lowest point on its way up, its total acceleration is (-22.5 i + 20.2 j) m/s2. The Attempt at a Solution Determine the magnitude of its radial acceleration. My...

Hi, I'm not sure this falls under the homework category, but I posted this here because I think this is more of an insight question than a question for help on how to solve the excercise (which I have). I am reading Sadiku's Elements of Electromagnetism. There is an exercise reads something...

Hi, I hope I chose the right forum for this topic. I'd like to show you an interesting property of orbiting bodies. I don't want you to solve it for me, I just thought the result is so beautiful that there must be simpler answer than just mathematically calculate it (I haven't managed to Google...

I'm looking to design a radial turbine to deliver 5 watts from compressed air (60-90psi) at 20,000 to 40,000 RPM. 30% efficiency would be suitable. I reviewed related patents-got little from them. I also reviewed my college textbooks, but they address incompressible, momentum transfer...

Homework Statement Assume that a point on an ellipse is described by the vector r=m(a\cos{\theta},b\sin{\theta}), where 0\leq m\leq 1 and that the vector is rotating in the clockwise direction at constant tangential velocity W when m=1. The problem is to find the velocity W(m). Also...

Homework Statement I need to calculate the tangential and radial force acting on a shaft so i can specify the correct bearings to use, however i don't know of any relevant formulae to calculate these, can anyone help? Power through the shaft is 1000w RPM is 130 Force acting vertically...

I have a u-shaped t-beam, and I am trying to calculate the radial stress where \theta=0 degrees. I have calculated \sigma\theta_{} but I am unclear on how to treat the varying thickness of the cross-section when integrating with respect to radius.

Hello, This is my problem and the solution from the book. I don't understand how they came to the solution. I believe it's wrong and I offer my own solution(but incomplete). I would appreciate if you could explain how they arrived to their solution or if I'm right. Thanks:) Please see below...

i now need to integrate the time-dependent schrodinger equation in 2D the potential is rotationally invariant and so is the initial wave function thus the symmetry of the initial wave function will be preserved in time Instead of a 2D equation, i now only need to integrate a 1d equation...

Homework Statement A 66-cm-diameter wheel accelerates uniformly about its center from 120 rpm to 260 rpm rpm in 4.9 s. Homework Equations a_t = r\alpha a_c= r\omega^2 a= a_r+a_t The Attempt at a Solution I have discovered that: \alpha = 3.0 \frac{rad}{s^2} and a_t =...

Homework Statement Compute the form factor of rho(r) = rho0 * exp[-ln2*r^2/R^2] where rho0 and R are constants. Homework Equations F(q) = 4pi/q \intsin(q*r)rho(r)rdr where the limits of integration run from 0 to \infty The Attempt at a Solution This is probably more of a...

Homework Statement A train slows down as it rounds a sharp horizontal turn slowing from 90.0km/h to 50.0km/h in the 15.0s that it takes to round the bend. The radius of the curve is 150m. Compute the acceleration at the moment the train reaches 50.0km/her. Assume it continues to slow down at...

Homework Statement A particle is moving clockwise in a circle of radius 2.50m at a certain instant in time its total acceleration is 15m/s^2. In the picture it shows the angle between the acceleration vector and radius is 30 degrees, and also there is a velocity vector with no value attached...

Homework Statement As a locomotive rounds a circular curve of radius 1.80 km, its speed is increasing at a rate of 0.440 m/s2. An instrument in the cab (an accelerometer) indicates that the magnitude of the locomotive's total acceleration at a particular instant is 0.680 m/s2. What is the...

I am solving the Hydrogen wavefunction using FORTRAN. Now using the Euler method, I am given a solution to match which is given by u10(r) = 1.06r*exp(-3.74r) (where unl(r) = rRnl(r) in general) which says it has a normalisation chosen to match what i should get from my code. Then I use the...

I am solving the Hydrogen wavefunction using FORTRAN. Now using the Euler method, I am given a solution to match which is given by u10(r) = 1.06r*exp(-3.74r) (where unl(r) = rRnl(r) in general) which says it has a normalisation chosen to match what i should get from my code. Then I use the...

Homework Statement This is not like a wheel where distance does not matter because a particular point will pass at the same time no matter how far down or up the wheel. In this experiment, I used a string attached to a stopper (at the top) with a washer (on the bottom). There was a glass...

In Wheeler and Taylor's 'Exploring Black Holes', on pages 3-12 and 3-13, the bookkeeper measure of radial velocity (i.e. radial velocity as measured from infinity) is derived. Basically the equation for 'Energy in Schwarzschild geometry' is established-...

I find it helpful to conceptualize radial redshift as nothing more than a longitudinal stretching out or elongation of an incoming light beam segment, as measured in the observer's rest frame. For example, a light beam segment which has been redshifted by a factor of 2 has been stretched to...

I'm doing a question on a 3D isotropic harmonic oscillator. At one point I need to find write the radial component of del^2. Lecturer has written \frac{1}{r^{2}} \frac{d}{dr} \left( r^{2} \frac{d}{dr} \right) where the del^2 used to be in the set of equations...

I'm doing a question on a 3D isotropic harmonic oscillator. At one point I need to find write the radial component of del^2. The lecturer has written 1/r^2 * d/dr * (r^2 * d/dr) I don't understand cause it looks like he hasn't actually changed anything, r^2 over r^2 ?

A projectile is shot directly away from Earth's surface. Neglect the rotation of the Earth. What multiple of Earth's radius RE gives the radial distance (from the Earth's center) the projectile reaches if (a) its initial speed is 0.758 of the escape speed from Earth and (b) its initial kinetic...

[b]1. The radial distribution function for the 1s orbital of the hydrogen atom is given by the equation below. Where a = the Bohr radius. What is the most probable distance from the nucleus for an electron in this orbital? [b]2. P(r) = 4r^2 (1/a)^3 exp(-2/a) [b]3. Setting dP/dr = 0...