deriving Definition and 1000 Threads

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...

This is essentially the problem. And this is what I did. Realizing the following: E = -▽V I simply took the derivative in regards to the vertical component, in this case "a". So: -dV/da [the above formulae] And I got the following: Κλl/(a sqrt(l^2+a^2)) Does that seem about right...

Homework Statement The pressure of a non-interacting, indistinguishable system of N particles can be derived from the canonical partition function P = k_BT\frac{∂lnQ}{∂V} Verify that this equation reduces to the ideal gas law. The Attempt at a Solution I have a very poor...

Hi all, First, I hope this is in the right place, apologies if it isn't. I'm looking into the possibility of deriving sound from the simulated actions of simple bodies in a 3D space. As a toy example of my aim, I hope to be able to compute the sound that would be generated by a metal...

Homework Statement Derive equation below. It is the potential energy of an electron inside a nucleus assumed to be a uniformly charged sphere of R. Homework Equations V'(r) =( -Ze2/4∏ε0R)(3/2 - (1/2)(r/R)^2) The Attempt at a Solution So I understand that I need to find the ∫ from infinity...

Homework Statement 1. Suppose two masses are arranged as shown and released from rest. There is no friction. Suppose we have a certain mass m1 and we want to cause a certain acceleration a. How big should m2be? (In other words, derive a formula for m2in terms of m1, a, and g.)...

So, there are two things in Quantum Mechanics that I understand are axioms: the first is the schrodinger equation, which cannot be derived. Okay fine, we have to start somewhere. The second axiom is that the integral from a to b of the wavefunction-mod-squared gives the probability of finding...

So i was wondering how the curl of the magnetic field is derived since Feynman just introduces it from nothing in his second volume of Feynman's lectures on physics: c2∇xB=j/ε0 or the other one where ∇x B=μ0j

Here is the question: I have posted a link there to this thread so the OP can view my work.

On the book "Introduction to Solid State Physics" by Kittel, on page 98 he derived the roots for optical and acoustical branches for the equation: M_1 M_2 \omega^4-2C(M_1+M_2)\omega^2+2C^2(1-cos(Ka))=0 where the roots are: \omega^2=2C(\frac{1}{M_1}+\frac{1}{M_2}) and...

so we used an equation in class to basically describe the relationship between some quantities of a vibrating string held fixed at both ends. and i noticed (just now...) that this was.. well.. i don't want to say that it's 'wrong' yet but, the expression does not make sense to me; and just to...

Well, I was doing a problem the other day, inserting the complete interaction QED Lagrangian into the Euler-Lagrange equations, in order to obtain the field equation governing the interacting electromagnetic field, with the Dirac field. The problem is that, by doing so, I got the equation, but...

Hi When we talk about shear stresses in a fluid, we find that the shear stress is given by \tau_{xy} = \mu(\partial_y u + \partial_x v) = \tau_{yx} This relation we get when only looking at one side of our fluid-"cube". Now, in order to take into account the opposite side we assume that the...

Homework Statement By considering small changes in enthalpy, and using the central equation, derive the Maxwell relation \left (\frac{\partial S}{\partial V} \right )_{T}= \left (\frac{\partial p}{\partial T} \right )_{V} Homework Equations H=U+pV dU=TdS-pdV The Attempt at a...

Homework Statement I have a 13 foot long beam supported by a pin at x = 0 feet and a roller at x = 9 feet. There is a triangular distributed load of 50 lb/ft from 0 ft to 9 ft. (Increasing as it approaches 9 ft) At the end of the beam there is a moment of 200 lb-ft counter-clockwise.Homework...

Lately I have been interested in the many-worlds interpretation, and in particular the way it is described by Wallace in his latest book The Emergent Multiverse. In the book he tries (or succeeds) to derive the Born rule from unitary dynamics by using game-theoretic arguments. But for this he...

I have been trying to derive the different ultimate 'fates' of the universe from Friedman's equations, for the different possible values of k (shape parameter) and ##\Lambda## (cosmological constant). There are nine possibilities, according to whether each of k and ##\Lambda## are negative...

Orthogonality of spherical bessel functions Homework Statement Proof of orthogonality of spherical bessel functions The book gave \int_{0}^{a}\int_{0}^{2\pi}\int_{0}^{\pi} j_{n} (\lambda_{n,j}r) j_{n'} (\lambda_{n',j'}r) Y_{n,m}(\theta,\phi)\overline{Y}_{n',m'}(\theta,\phi) \sin\theta...

Homework Statement Find vrms from the Maxwell speed distribution. Basically what I need to solve is the integral a\int_0^∞ \! v^4e^{xv^2} \, \mathrm{d}v Where ##a## and ##x## are constants. Homework Equations $$a\int_0^∞ \! v^4e^{xv^2} \, \mathrm{d}v $$ Where ##a## and ##x## are...

Homework Statement Derive m*= mM/(m+M) *hint* total angular momentum Iω=m*r2ω equals the sum of the individual angular momenta, where r = re + rn; re and rn are the distances of the electron and nucleus respectively from the center of mass. Homework Equations Angular Momentum = mvr...

So,here we have a graph.For every unit of 1(x axis),the unit of the previous y-axis is multiplied. Like this. (0,2),(1,4),(2,8),(3,16)... I don't know how the formula will be,and had never seen this kind of graph. The y seems to be a geometric sequence,on which we can use, ## ar(n-1) ## .r is...

hello, im trying to do this homework, where i have to derive Plancks constant using an experiment where we used some LED lights of different wavelengths to work out voltage at different wavelengths. From that i worked out the frequency and ekmax of the electrons given out. however i have no...

Homework Statement Question is hereHomework Equations Shown in the image, but just to restate: Vc(t) = A+Be^(-t/τ) n/m=e^-1 OR p/m=1-e^-1 The Attempt at a Solution First thing I tried to do was solve the Vc(t) equation for e, which comes out to e=(-A/B)^(-τ/t). I'm not even sure if...

Hi Please see table below GDP growth rates of a group 5 countries. I am trying to derive some conclusions from this small sample. 1. can I conclude that countries in the group have very similar growth rates and there is no significant difference between their growth rates? 2. As...

I'm looking at this scenario where a car is moving and then shifts into neutral. Knowing the initial velocity, how can I derive a differential equation? I know the air drag and the frictional force... are there any other forces, like gravity, that should be included to make it realistic? I...

I may be being stupid here... But I'm trying to derive such an equation to no avail. Maybe such a formula requires more than one variable - but I would like to easily display this graphically. To start out the derivation I stated that the Surface Velocity = (2pi/T)-(v/r) where v/r=angular...

original question: Consider light passing from one medium with index of refraction n1 into another medium with index of refraction n2. User Fermat's principle to minimize time, and derive snell's law (n1sintheta1=n2sintheta2). here is part of the solution key http://i.imgur.com/S1Pg9jC.png...

Homework Statement We want to fin an expression for \theta, the Rutherford scattering angle. I have an expression that I derived for a hyperbolic trajectory, of the form \frac{(x+x_0)^2}{A^2}-\frac{y^2}{B^2} = 1. We wanted it in terms of α, ε, where α is a constant ( \alpha =...

I am currently redoing grade 11 physics and they have introduced the following formula, \Delta d = v_1\Delta t + \frac{1}{2}a\Delta t^2 I am trying to find this equation using calculus. So from what I understand, \Delta d is the area under the curve for v(\Delta t). We can define v(\Delta...

https://dl.dropboxusercontent.com/u/22024273/vectorpotential.png In the above passage, can someone explain to me where (3.102) comes from?

Homework Statement http://puu.sh/4M7BE.png Homework Equations ln(ax) = x*ln(a) The Attempt at a Solution ln(y) = cos(x)*ln(ln(x)) dy/dx * 1/y = -sinx*ln(ln(x)) + cosx/(x*lnx) No clue how to solve this, there's no ln(ln(x)) in the possible answers Attempt 2 y =...

Homework Statement In a damped harmonic oscillator, show that |R(\omega)|^2 = \gamma at full width half maximum. 2. My attempt at a solution This is another one of those questions that I feel like I am almost there, but not quite, and it's the math that gets me. But here goes: For a...

Homework Statement For some work I am doing I wish to be able to define the potential distribution as a function of the radius (ρ) between two concentric electrodes. Homework Equations One solution (from reliable literature) defines the varying radial potential as: V(ρ)=2V0(ρ0/ρ...

Problem: Material scientists have discovered a new fluid property called "radost" that is carried along with a fluid as it moves from one place to the next (just like a fluid's mass or momentum). Let ##r(x,y,z,t)## be the amount of radost/unit mass in a fluid. Let ##\rho(x,y,z,t)## be the...

Hello, I have few question for deriving the Lorentz transformation (LT): While deriving the LT, we draw a graph as x,y,z in one frame of reference and x',y',z' in the other frame of reference as S and S' as two frames of reference. Now the factor ct comes in, which is the flash of...

Homework Statement OK, we've been asked to derive the equations of motion in spherical coordinates. According to the assignment, we should end up with this: $$ \bf \vec{v} \rm = \frac{d \bf \vec{r} \rm}{dt} = \dot{r} \bf \hat{r} \rm + r \dot{\theta}\hat{\boldsymbol \theta} \rm + r...