deriving Definition and 1000 Threads

Hello, I think I've got the right idea on how to perform this question but I just need a little bit of help. Homework Statement Show that for a rigid body rotating with angular velocity \omega the energy of rotation may be written as: E = \dfrac {1}{2}I\omega^{2} where the moment of...

Homework Statement For 0<t<1, v(t) = t +3 For 1<t<2, v(t) = 5-t Assume x(o)=0 A) Draw corresponding displacement and acceleration diagrams. B) Determine the equation for each segment Homework Equations Acceleration is the derivative of velocity. Velocity is the derivative of...

Hi Sorry this may be an obvious one...can anyone help me with getting from the first to the second equation below? I'm particularly stuck with manipulating the terms inside the summations formulas. I can derive to here: \sum_{i=1}^{N}x_iy_i - N\bar{x}\bar{y} - \left(...

Homework Statement Using equations #1 and #2 to derive equation #3 Homework Equations #1- ∆x = (b/2)theta #2- ∆z= L (2theta) #3- ∆x= ∆z b/4L The Attempt at a Solution Now I set equations #1 and #2 equal to each other, but I'm not sure how the thetas end up cancelling or if I'm even...

HI I need help with the steps in between? I am totally confused... So, how to derive the final equation from equation 1 and 2 m1v1i+m2v2i=m1v1+m2v2f (Equation 1) 1/2m1V1i^2+1/2m2v2i^2=1/2m1v1f^2+1/2m2v2f^2 (Equation 2) v1i-v2i= -(V1f-v2f) ( Final Equation)

Homework Statement I need to derive an error equation from the following equation... \frac{e}{m} = \frac{2V}{B^{2}R^{2}}Homework Equations Just... basic... derivation rules...The Attempt at a Solution I did try, just don't know how to put the stupid attempt in LaTeX... I'm stuck at the "2V"...

Homework Statement I need to find the Planck's law: R(\lambda)=\frac{2hc^2}{\lambda^5}\frac{1}{e^{\frac{hc}{\lambda kT}}-1} Homework Equations The Attempt at a Solution I've done most of the derivation, but I got stuck with an integral: R(\lambda)=\frac{1}{4\pi^3 \hbar^3 c^2}...

Homework Statement 2x^2+5xy-y^2=1 Homework Equations d/dx(f(u)x))=df/du * du/dx The Attempt at a Solution i got (2y-4x)/5x but I'm almost certain that its wrong...can anyone help me?

I am trying to derive the electromagnetic wave equations from Faraday's law of Induction, and the Ampere-Maxwell law. But, I am having a problem with the 1/c^2 disappearing. This is what I am using: \nabla\times\vec{B}=\mu\vec{J}+\mu\epsilon\stackrel{\partial\vec{E}}{\partial t}...

Hi all, There are a few doubts I hope I can get enlightened. If we were in a lab in outer space, free of gravitational influence and the lab accelerates downwards, what will we experience? do we 'move' to the top of the lab? What I'm confused about also is, why is that when you have an...

When setting up this derivation one assumes a chain of identical atoms. The interatomic interaction between atoms is short ranged and so only affects neighbouring atoms (see Hook and Hall, "Solid State Physics" chapter 2.3.1). The potential V(r) is expanded as a taylor series about r = a to...

Homework Statement Find the commutators [P^\sigma,J^{\mu \nu}] The answer is part of the Poincare algebra [P^\sigma,J^{\mu \nu}]=i(g^{\mu \sigma}P^\nu-g^{\nu \sigma}P^\mu) If someone can convince me that \partial_i T^{0\mu} = 0, (i.e. the energy-momentum tensor has no explicit spatial...

When working with Fourier transforms in Quantum mechanics you get the result that \int_{-\infty}^{\infty}e^{-ikx}e^{ik'x} = \delta(k-k') I understand conceptually why this must be true, since you are taking the Fourier transform of a plane wave with a single frequency element. I have also...

Homework Statement Using the normal distribution for different modulation techniques over rayleigh fading , we have to derive SNR values for different Diversity techniques such as selection combining, Equal Gain Combining and Maximal Ratio Combining. Now for Non-coherent BPSK I have to...

Homework Statement Derive the error expression \delta v_{}x from the equation v _{x}=\frac{s}{sqrt(\frac{2h}{g})} The Attempt at a Solution I've derived error expressions before, but I have a history of getting the calculations right and the error equations wrong. So, if possible I'd...

Homework Statement Derive an equation for velocity based on time with drag. Homework Equations The equation is: v(t) = F/b (1 - e^(-bt/m)) The Attempt at a Solution There's some math on paper, but I got down to: F - bv = ma a = dv / dt F - bv = m*dv/dt dt = m*dv / (F -...

Homework Statement If a string wound around a fixed circle is unwound while held taut in the plane of the circle, its end P traces an involute of the circle. In the accompanying figure, the circle in question is the circle (x^2)+(y^2)=1 and the tracing point starts at (1,0). The unwound...

I am supposed to derive this equation: g=aave(M + m / m) It gives me two pairs of equations: T1-Fr = Ma1 mg-T1= ma1 and T2 + Fr = Ma2 mg - T2 = ma2It also says, "hint: for the first pair of equations, eliminate the unknown tension. Do the same for the second pair of equations. In this new...

How does one begin to derive the resonant frequencies of a multiple mass mass-spring system? (3-mass system) OK, so deriving this isn't a homework problem. I'd just like to know how. It's been a couple of years since I've taken a physics course. I was asked what the resonant frequencies of each...

Wikipedia's 'special relativity' entry gives the following relationship between force, acceleration and velocity: \vec f=\gamma m \vec a + \gamma^3 m \frac {\vec v \cdot \vec a}{c^2}\vec v but without derivation. Could someone tell me how one arrives at this? Thanks.

Homework Statement Find the impedance of the circuit (R and L in series, and then C in parallel with them). A circuit is said to be in resonance if Z is real; find ω in terms of R, L, and C at resonance. Here is the circuit: http://img382.imageshack.us/my.php?image=g...ccircuitgf5.png...

Homework Statement I have been given these two equations: x=2acos^2(x) , y = 2a(cos(x))(sin(x)) where a ranges from 0 to 5 and -2π < x < 2π I need to prove that these equations (when you plug in values for x) create points that when plotted, give you a circle with center (x-a) and radius a...

Homework Statement A thin, circular plate assumed to lie on the xy-plane is rotating about its center, located at (0, 0), with angular speed ω. (ω > 0 means that the plate is rotating in the counterclockwise direction.) Show that the velocity field of of this plate is given by v(x, y) =...

I'm supposed to derive this monster! \frac{1}{2} + \frac{2}{\pi} \sum^{\infty}_{k = 1}\frac{1}{2k-1}sin(2k-1)x = \left\{^{0 \ for \ -\pi < x < 0}_{1 \ for \ 0<x<\pi} I don't even know where to start right now. And no examples to work from. Can anyone get me started? the Chapter is on...

deriving identity - need help! Homework Statement Derive for S^{p}_{n} = 1^p + ... + n^p the identity (p+1)*S^{p}_{n} + (p+1 choose 2)*S^{p-1}_{n} + ...+S^{0}_{n} = (n+1)^(p+1) - 1 Homework Equations Um, I know that the S^{1}_{n} = n(n+1)/2 S^{2}_{n} = n(n+1)(2n+1)/6 S^{3}_{n} =...

deriving identity - need help! Homework Statement Derive for S^{p}_{n} = 1^{p} + ... + n^{p} the identity (p+1)*S^{p}_{n} + (p+1 choose 2)*S^{p-1}_{n} + ...+S^{0}_{n} = (n+1)*^{p+1} - 1 Homework Equations Um, I know that the S^{1}_{n} = n(n+1)/2 S^{2}_{n} = n(n+1)(2n+1)/6...

Homework Statement Derive: \left(\frac{\partial C_{P}}{\partial P}\right)_{T} = -T \left(\frac{\partial^2 V}{\partial T^2}\right)_{P} Homework Equations I have already derived that C_{P} = C_{V} + \left[\left(\frac{\partial E}{\partial V}\right)_{T} + P \right] \left(...

Could someone show me exactly how to derive the quadratic equation from the least squares method? I have no idea where to start. I will appreciate it very much. Thankyou.

hello. i need help deriving trig formulas. the first problem i most derive is 51. sin^2 x + cos^2 x = 1 i can use these identities: a. sin(-x) = -sinx b. cos(-x) = cos(x) c. cos(x+y) = cosxcosy - sinxsiny d. sin(x+y) = sinxcosy + cosxsiny thanks for any help

Homework Statement I apologize for the blurriness in my title, I couldn't find anything better to fit within the length limit. The problem I'm stuck with, paraphrased, is to derive the formula for the diffraction pattern of a double slit, as found in the Young experiment, from the Fraunhofer...

Homework Statement "starting from the definition of tanhx in terms of exponentials, prove that... arctanh(x)=1/2log((1+x)/(1-x)) This is such a simple equation but I'm having a hard time proving it, can anyone help? Cheers Homework Equations The Attempt at a Solution

I am having trouble with this derivation. This is where I am at: \frac{d \left< p \right>}{dt} = \int \left[ \left( -\frac{\hbar^{2}}{2m}\frac{\partial^{2} \Psi^{*}}{\partial x^{2}} + V\Psi^{*} \right) \frac{\partial \Psi}{\partial x} + \frac{\partial \Psi^{*}}{\partial x}\left(...

On pages 16-17 of Griffith's Intro to QM, he writes the following: \frac{d\left\langle x \right\rangle}{dt}= \int x \frac{\partial}{\partial t}|\Psi|^{2} dx = \frac{i\hbar}{2m}\int x \frac{\partial}{\partial x} \left( \Psi^{*}\frac{\partial\Psi}{\partial x}- \frac{\partial\Psi^{*}}{\partial...

this lab is very similar to mine basically i can only seem to derive a portion of the formula, I=mgb/al - mb^2 where b- radius, g-gravity, al- angular acceleration. I do not get the right answer: here is what i did do however, Fnet=ma T-mg=-ma (acceleration is downwards) so T=(mg-ma) so then...

Homework Statement How would I derive Gauss' law for gravity from Newton's law?Homework Equations \mathbf{g}(\mathbf{r}) &=& -G\frac{m_1}{{\vert \mathbf{r}\vert^2}}\hat{\mathbf{r}} to \nabla\cdot\mathbf{g} = -4\pi G \rhoThe Attempt at a Solution I have no reference material outside the wide...

So I am trying to derive the continuity equation: \frac{\partial}{\partial x^{\mu}}J^{\mu} = 0 From the Dirac equation: i\gamma^{\mu} \frac{\partial}{\partial x^{\mu}}\Psi - \mu\Psi = 0 And its Hermitian adjoint: i\frac{\partial}{\partial x^{\mu}}\overline{\Psi}\gamma^{\mu} -...

[SOLVED] Amperes Law Homework Statement Deriving the magnetic field through a solenoid. Homework Equations dB = mu0/4pi x Idlsintheta/ r^2 where I = current dl= a tiny change in length dB = a tiny change in flux density sintheta is the angle to the normal r is the radius mu0 is the...

It's been a while since I've taken calculus. I was going through the derivation of the work-energy theorem and came across this: dv/dt = (dv/dx)(dx/dt) which is supposed to be a result of the chain rule. Anyone care to explain and please simplify it as much as possible. Thanks!

Homework Statement If \Psi = f(x, y) and x = g(t), y = h(t), then (d\Psi / dt) = (p\Psi / px)(dx / dt) + (p\Psi / py)(dy / dt), where "p" symbolizes the partial derivative here and throughout the rest of this posting. Derive the phase velocity equation +/- v = -(p\Psi / pt) / (p\Psi / px)...

Hey, Homework Statement How do you derive the equations of the parabola from the general equation of a Conic Section? Homework Equations General Equation of a Conic Section, {{{A}{{x}^{2}}}+{{B}{x}{y}}+{{C}{{y}^{2}}}+{{D}{x}}+{{E}{y}}+{F}} = {0} Where (for a parabola)...

Here are some papers on the covariant entropy bound conjectured by Raphael Bousso http://arxiv.org/abs/hep-th/9905177 http://arxiv.org/abs/hep-th/9908070 http://arxiv.org/abs/hep-th/0305149 It would be a significant development if the conjectured bound could be proven to hold in LQC...

As i know there are several diffrent way to derive the canonical equations. Some of them starts from a physical principle like Hamilton's principle or the Lagrange equations. But it can be derived also by simply make a Legendre transormation on the Lagrange function and then make...

help deriving this elliptical orbit equation?? Hi guys, this is my first post on these boards. just found out about this forum and I am really happy because i often find i need a place like this to ask questions and my prayers are answered! im a physics/computer science major in my second year...

Homework Statement An object of mass m is at rest at equilibirum at the origin. At t=0, a new force \vec{F}(t) is applied that has components F_{x}(t) = k1+k2y F_{y}(t)=k3t where k1, k2, and k3 are constants. Calculate the position r(t) and velocity v(t) vectors as functions of time. Homework...

Why does du/dT = Cv, and same for Cp? Also, i don't understand how Cp/Cv = v, where v is the specific volume. It is derived from: Cv + R = Cp, how is PV=nRT used to get from Cv + R = Cp to Cp/Cv = v? I know n is replaced by m/M to leave Pv=RT where R would equal R(universal gas const)/M...

So in my book, it derives the expression for power in a traveling transverse mechanical wave. P= Sqrt[(mu)F].(omega)^2.(A)^2 It reduces this from: P=k^2.omega^2.F.A^2.(sin(kx-omega.t)^2 Where all symbols are the standard ones in dealing with waves. Could someone please go thru how it...

Derive the following equation: (mV^2/r)cos(x) = mgsin(x) I don't know how you would exactly derive the equation but you can simplify it to: tan(x)mg = mV^2 /r You can also divide by the m and get tan(x)g = V^2/r ... Any help is appreciated.

Homework Statement I am doing some research and reading this: http://www.csuohio.edu/ece/theses/2004/Bhavin.pdf I don't understand how the equation 4.1.11 on page 67 is derived. Can anyone help clarify? Homework Equations (As in the pdf file) The Attempt at a Solution I have...

can anyone help me derive the poynting vector from energy density of electromagnetic waves? and how we obtain average value <S> thanks

I knew i should have paid more attention in class =/ anyways, We have been studying Newton's second law. And I have a question on my lab that asks for me to "derive equation for a (acceleration) vs F (force) and a (acceleration) vs m (mass)" a vs F and a vs M are two graphs which we did...