deriving Definition and 962 Threads

Homework Statement To go from Euler's theorem : to angular velocity as shown: Homework EquationsThe Attempt at a Solution I'm curious how to begin. I can not see the connection! I know w = dtheta/dt, but not sure how to approach this. It has to be more than just differentiate the first...

[Mentor's note: this thread was moved from a non-homework forum, therefore it does not use the normal template for homework questions] What is the speed of the electron in terms of the speed of the light when it is in the n = 3 state in the Hydrogen atom? I started with this equation to find...

Hello, I have a simple question about deriving $$g_{ij} \frac{\partial x^i}{\partial t}\frac{\partial x^j}{\partial t}$$ with respect to time t. I have noticed that the first term after derivation turns out to be$$ \frac{\partial g_{ij}}{\partial x^k} \frac{\partial x^k}{\partial...

Homework Statement Hello! I am trying to derive the ground state enegry of a hydrogen atom, and have come to U=\frac{-mk_{0}^{2}Ze^{4}}{n^{2}\hbar^{2}} Problem is, I know there should e another factor of 2 in the denomenator because I get the ground state energy of hydrogen as being 27.145eV...

Homework Statement Hi! Not sure if I'm posting in the right section, this problem is from a course in scientific computing. Anyway, we're considering a set of PDEs: u_t + Au_x = 0 \quad 0<x<1, \ t>0 \\ u(x,0) = f(x) \quad 0 \leq x \leq1 \\ u_1(0,t) = 0 \quad t \geq 0 \\ u_2(1,t) = 0 \quad t...

I understand the derivation of gravitational potential energy when an object is moved away from Earth but when I try to derive the formula for gpe by considering a test mass moving from infinity to r then I end up with a positive gravitational potential energy. Because integrating F.dr from...

Hello everyone, I have a problem with deriving following equality: \begin{equation} u^{s}(p) \bar{u}^{s}(p) = 1/2 ((\slashed{p} + m)(1+\gamma^5 \slashed{s})) \end{equation} where s is spin 4-vector. I know how to calculate this tensor product when there is spin sum in front of it, but without...

Hello there, Plack law of radiation $$ B(\nu) = \frac{2\,h\,\nu^3}{c^2(e^{h\nu/kT}-1)} $$ I want to show that for small frequencies, Reyleigh-Jeans law: $$ B(\nu) = \frac{2\nu^2kT}{c^2} $$ is correct. I take the limit of Planck law as ##\nu \to 0## using l'hopital rule: $$ \lim_{\nu \to 0}...

Can someone either derive or point me to a derivation of Møller's formula for the relativistic minimum radius of a rotating body? I've been searching for about an hour and it's driving me crazy! The only "minimum radius" equation I've seen imposes the speed limit c on a classical rotating body...

When one derives the ultraviolate catasrophe one looks at a cavity of perfectly conducting walls and with standing electromagnetic waves. Since these waves must vanish at the walls of the cavity, the wavelengths of the radiation is restricted according to the dimensions of the cavity: for...

If we write the Biot Savart law as B(r)=μ0/4π∫(J(r')xn/n2)dV' where B is the magnetic field which depends on r=(x,y,z), a fixed point, J is the volume current density depending on r'=(x',y',z'), and n=r-r', a vector from the volume element dV' at r' to the point r. Note we integrate over the...

Homework Statement How does one get the r" equation from r'? Homework Equations r = distance v = r' = ds/dt a = r'' = dv/dt chain rule, dy/dt = dy/dx * dx/dt The Attempt at a Solution I can easily get to r' from r using the chain rule but how do you derive r" from r'? How do you apply...

Homework Statement Derive an equation relating the angle of incidence and the angle of refraction as light travels from air to glass. Do it in the form of Θ2/Θ1 = expression Homework Equations I think the equation to use here is Snell's law. Right? n1sinΘ1 = n2sinΘ2 n1 = nair =...

Homework Statement It is not an official question but a request for pointers. I am trying to derive the Lorentz time equation to understand the intuition behind it. My math skills are not very good so it might be an obvious question for you. Please see below for my attempt. The variables are...

Homework Statement A and B are two unit vectors in the x-y plane. A = <cos(a), sin(a)> B = <cos(b), sin(b)> I need to derive the trig identity: sin(a-b) = sin(a) cos(b) - sin(b) cos (a) I'm told to do it using the properties of the cross product A x B Homework Equations A x B =...

Homework Statement I'm getting really confused when it comes to electric potential. The definition I am using is 'the work done per unit charge on a small positive test charge when it is moved from infinity away to a point'. My first problem is that I'm not sure whether 'the work done' refers...

Homework Statement How to derive W=(.5*I)*((ωf^2)-(ωi^2)) from W=τ*(θ) Homework Equations The two equations seen above (big W is work; little w is rotational velocity, τ is torque, alpha=rotational acceleration). s=r*θ a=r*(alpha) (ωf^2)-(ωo^2)=2*(alpha)*(θ) F=r*τ F=ma...

In order for the light to take the same amount of time for both paths in the interferometer, simple geometry implies that the ratio between length and width will have to decrease. A straightforward derivation gives L/W=Sqrt(1-v^2/c^2) where the velocity v is in the direction of the length...

Homework Statement Inscribe N chords of equal length within a circle of radius r. A body of mass m travels at constant speed v along the chords and is perfectly reflected in each collision with the circle (there is no momentum change tangent to the circle). Show that the radial momentum change...

I'm an engineering student, and I'm making a formula for the volume of liquid in a cylinder that is cut in half diagonally. r is the radius, h is the height from the bottom to the top of the sloped flat bottom, and L is the height of the water within the cylinder. So when L = h you would expect...

Hello everyone. I am attempting to teach myself about special relativity, and have learned a derivation for the Lorentz transformation. Before I go any farther I want to clear up the parts I don't understand right now and check that I am correct about the parts I do understand. Here I will...

To start, we have: ψ=e^{i(kx+wt)} ψ_x=ikψ ψ_{xx}=-k^2ψ λ=\frac{h}{p} k=\frac{2π}{λ} E=\frac{p^2}{2m}+V Then, multiply both sides of energy equation by ψ to get: Eψ=\frac{p^2}{2m}ψ+Vψ And replace -k^2 in the wave equation with -\frac{p^2}{hbar^2}. Then plug into energy equation for p^2 to get...

Hi, I'm trying to derive the displacement of an object with proper acceleration (constant) α. t is our laboratory time. The goal: x(t) = {1 \over α} [ \sqrt{1+α^2t^2} -1 ] How to approach this? :( Note for anyone who's wondering: no, this is not homework...

Hey guys, as this is a basic QFT question, I wasn't sure to put it in the relativity or quantum section. Since this question specifically is about manipulating tensor expressions, i figured here would be appropriate. My question is about equating coefficients in tensor expressions...

I'm having problems getting going on the following question, any help appreciated: As part of his training an athlete usually runs 80 km at a steady speed of \(v\) km h. One day he decided to reduce his speed by 2.5 km h and his run takes him an extra 2h 40 mins. Derive the equation...

Hi. I have no idea how to do this. It's complicated because the length here is a variable. I posted the same question before but there was a little mistake so I am reposting this again. The picture below shows the potential due to ring charge. Please show the full steps of deriving the...

The picture shows the potential due to ring charge. Please show the full steps of deriving the equation of electrical potential. I don't know how to start at all. NOTE: The electric potential of the revolving symmetrical ring electric charge related to the axis z as depicted in the diagram...

I'm having difficulty deriving a quadratic from the info in this question: A train usually covers a journey of 240 km at a steady speed of \(v \text{ kmh}^{-1}\). One day, due to adverse weather conditions, it reduces its speed by 40 \text{kmh}^{-1}\) and the journey takes an hour longer...

Hello. I was reading Hyperphysics website and could not get one particular part. I am providing a picture of the equation I am having trouble with: http://i.snag.gy/W3CC3.jpg The particular part that puzzles me is the relation around the third equation sign. From the formula there one can think...

First, I'm a second year high school physics student so my thinking may be half-baked. I was wondering what motion a piston would exhibit if it was the frictionless lid of an ideal gas cylinder with a constant amount of air, and if it was pushed or pulled a little bit. There would be a...

hey guys! I'm really confused as to what this question is trying to ask me! can someone help me out :) Air pressure decays approximately exponentially at about 0.4 per cent for each rise of 30 metres above sea level. If we let p = p(h) denote air pressure (measured in some appropriate units) at...

I saw a joke crib sheet for a physics class that said "F=ma, derive the rest," but is it actually possible to derive at least electricity and magnetism questions from Newton's second law?

Good afternoon, I am making way through this paper and I am having trouble "seeing" how the linear velocity AE is derived at the top of...

Hi, This is a worked example in the text I'm independently studying. I hope this isn't too much to ask, but I am stupidly having trouble understanding how one step leads to the other, so was hoping someone could give me a little more of an in-depth idea of the derivation. Thanks. Homework...

consider the following model for aggregate claim amounts S: S=X1+X2+...+XN where the Xi are independent, identically distributed random variables representing individual claim amounts and N is a random variable,independent of the Xi and representing the number of claims.let X has ìx and...

Homework Statement I need to derive the moment of inertia of a thin rod with its axis of rotation at the end of the rod. http://en.wikipedia.org/wiki/List_of_moments_of_inertia The third one. Homework Equations I = mr^2 The Attempt at a Solution I completely understand how the...

1.This equation in the link below refers to the small angle approximation regarding deriving the wave equation from Newtons laws from small amplitude waves in a single string with fixed tension. 2.http://imgur.com/NGSwzcl 3. I'm a bit rusty on the maths and have no idea how these...

Hello everyone, The problem I am currently working is exactly what is given in this link: https://www.physicsforums.com/showthread.php?t=554243 However, I do not understand why we integrate between 0 and infinity. What is the motivation for doing so?

Hi! As my professor is a bit crazy (in a good way), he derived Stefan-Boltzman's law in my intro thermodynamics class. However, since he introduced loads of concepts from statistical mechanics and such I got a bit confused on some points. Anyway: The first part of the derivation: My question...

Wrote my question up in Latex Update: I have corrected the mistake when I stated the "textbook" version of the equation that the problem requires to be used. I have reposted the pdf with the same name.

I would like to derive the surface area for an equation in the form of \(z = f(x, y)\). For example, if I have a sphere \((b^2 = x^2 + y^2)\), the surface area is circumference times arc length \((SA = 2\pi r\ell)\). Here I can take an arc and break it up into n parts to find the differential...

Homework Statement From Bohr’s model of hydrogen atom, derive the ratio of the electron velocity in the ground state of hydrogen atom to the speed of light, which is the fine structure constant α, in terms of fundamental physical constants such as h, m, and c. Homework Equations...

Homework Statement Using the formal limit definition of the derivative, derive expressions for the Fourier Transforms with respect to x of the partial derivatives \frac{\partial u}{\partial t} and \frac {\partial u}{\partial x} . Homework Equations The Fourier Transform of a function...

1.Homework Statement Derive the quadradic equation, ax^2 + bx + c = 0, using the fallowing method. 1. Divide by a, if a =/ 0. 2. Move the constant to the other side of the equation. 3. Square half the coeffecient of bx and add it to both sides, fixate the negative sign on -c/a. 4. factor the...

Homework Statement Show using Boltzmann's principle (S=k.lnW), show that with respect to changes in V and T: dS=k.N.\frac{dV}V{}+\frac{C.dT}V{T} Where W=T^{\frac{C}k{}}V^{N}The Attempt at a Solution S=k.lnT^{\frac{C}k{}}V^{N}=k.lnT^{\frac{C}k{}}+klnV^{N} S=C.lnT+N.lnV Now I know that the...

hey pf! i was hoping one of you could help me with deriving the navier stokes equations. i know the equations state something like this \sum \vec{F}=m\vec{a} and for fluids we have something like this for the forces: \underbrace{-\iint...

1. Deriving frequency in a beam equation, E=Young's Modulus, I = Moment of Inertia, m=mass, L=length, f=frequency. 2. Deriving this equation: (∏/2)√(EI/mL3) 3.(EI(∂4y/∂x4 = -m(∂2y/∂x2) ≈ EI(∂4y/∂x4+ m(∂2y/∂x2 = 0 Don't know where to go from here...

Hello, my timetabled experiments for lab work are a week or two ahead of my E&M course which means I'm doing the experiments before being introduced to the theory. As part of my prep work I need to come up with an expression for the total capacitance of a number of different circuits involving...

I am trying to derive the geodesic equation by extremising the integral $$ \ell = \int d\tau $$ Now after applying Euler-Lagrange equation, I finally get the following: $$ \ddot{x}^\tau + \Gamma^\tau_{\mu \nu} \dot{x}^\mu \dot{x}^\nu = \frac{1}{2} \dot{x}^\tau \frac{d}{ds} \ln \left|...

consider the following image (the red is the surface area element and the green is the differential element that I'm integrating over) when we derived this in class, we treated the area formed by vectors a and b, as the area of a parallelogram. the thing is, a and b should be at right...