deriving Definition and 962 Threads

Homework Statement I'm trying to derive the voltage waveform across the capacitor for a discharging capacitor that has been fully charged by a DC power supply ##v_0##, i.e. ##v_c(t=0)=v_0## and then at ##t=0## the switch is flipped and the capacitor starts to discharge. Homework Equations The...

Hi, I have a question Given the function LzYilm(θ,ϕ) =mħYilm(θ,ϕ) What steps can I take to confirm that Lz=ħ,0,-ħ

Homework Statement I am trying to derive the equation for the charge of a capacitor as a function of time: Q (t) = Qmax (1-e^(-t/tau). Homework Equations Kirchhoff's loop law I (t) = dQ(t)/dt Delta Vbat= Epsilon Delta Vresistor= -I*R = [-dQ(t)/dt]*R Delta Vcapacitor= Q/C Qmax = C*Epsilon Tau =...

Homework Statement Given that the potential of dipole is equal to: V(\vec{r})=\frac{\vec{p}\vec{r}}{4\pi\epsilon_0 r^3} show that the electric field is equal to: \vec{E}(\vec{r})=\frac{1}{4\pi\epsilon_0}(\frac{3(\vec{p}\vec{r})\vec{r}}{r^5}-\frac{\vec{p}}{r^3}) Homework Equations...

Homework Statement Homework Equations average speed = total distance/total time The Attempt at a Solution 24. [/B] The shortest road distance from Toronto City Hall to the Shaw festival theatre in Niagara-on-the-Lake is 131 km. a) First I will calculate the area of each rectangle using...

Hi everyone. I'm trying to derive an expression of the velocity of an object in free fall on Mars, and I am having trouble. Here is what I've done so far: Drag on Mars can be expressed as $$F_d = \frac{C_d A \rho_M v^2}{2}, $$ where C_d denotes the drag coefficient, A the reference area, and...

I posted a question about this yesterday, but realized I had made a stupid mistake in my derivation. Orbital dynamics: "The familiar arc-cosine form" That error has been corrected. I still have a deeper question. I believe this expression can be developed using the geometry of an ellipse in...

Hi, friends! I have been able to understand, thanks to Hawkeye18, whom I thank again, that, if ##\mathbf{J}## is measurable according to the usual ##\mathbb{R}^3## Lebesgue measure ##\mu_{\mathbf{l}}## and bounded, a reasonable hypothesis if we consider it the density of current, if...

Good day to you all, I could be asking too much here. I’m someone who prefers to understand formulas by deriving them from own made scenarios. In this case I was trying to derive the time dilation Lorentz formula using my own made up example and I wanted to know if I'm on the right track here...

Hi, friends! I have been struggling to understand the only derivation of Ampère's law from the Biot-Savart law for a tridimensional distribution of current that I have been able to find, i.e. Wikipedia's outline of proof, for more than a month with no result. I have also been looking for a proof...

I am trying to derive the geodesic equation using variational principle. My Lagrangian is $$ L = \sqrt{g_{jk}(x(t)) \frac{dx^j}{dt} \frac{dx^k}{dt}}$$ Using the Euler-Lagrange equation, I have got this. $$ \frac{d^2 x^u}{dt^2} + \Gamma^u_{mk} \frac{dx^m}{dt} \frac{dx^k}{dt} =...

So I am teaching myself physics in "Physics 1 For Dummies" and I have come across a chapter dealing with deriving equations, this one being the distance through using the average velocity. I have never derived equations before, so be easy on me! So basically it starts off with s=vt (distance...

Homework Statement Homework EquationsThe Attempt at a Solution So I am tasked with answer #3 and #4. I have supplied the indicated parenthesis of 8 also with the image. Here is my thinking: Take the Fourier series for |sin(θ)|. Let θ = 0 and we see a perfect relationship. sin(0) = 0 and...

I'm going through Ray D'Iverno's "Introducing Einstein's Relativity", and there is a step he makes in deriving the Lorentz transformations that doesn't seem necessary to me. So I'm not sure what I'm missing. He derives them from Einsteins postulates of relativity. From the postulate that the...

How is E=mc^2 derived from relativistic doppler effect? I looked up on wikipedia but it seems to have some errors. https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#Alternative_version

So there was a really old thread about this, but I don't think the matter was ever really resolved, which is why I'm making this thread now. I'm trying to derive the equation τ = Fd but I've run into a bit of trouble. I started with x=θr where x is the arclength on a circle (since any point...

I'm trying to figure out the effect of a force applied to a rotating body in 4+1 dimensions. A good place to start would be deriving the effect of forces in 3+1 dimensions. I have been looking around the Internet and even went to the local community college and checked out texts in the library...

Homework Statement I am trying to obtain the hermite polynomial from the schrødinger equation for a har monic oscillator. My attempt is shown below. Thank you! The derivation is based on this site: http://www.physicspages.com/2011/02/08/harmonic-oscillator-series-solution/ The Attempt at a...

So if I'm given a coordinate plane that graphs the position of a particle, how do you get the s(t), in respect to time if given a table of time intervals. Given: f(x) = -x^2 Needed: s(t)? v(t)? a(t)?

Homework Statement I am trying to get the hamiltonain operator equality for a rigid rotor. But I don't get it. Please see the red text in the bottom for my direct problem. The rest is just the derivation I used from classical mechanics. Homework Equations By using algebra we obtain: By...

I'm sure the inductor model, i.e. vL(t) = iL'(t)*L follows without directly from Faraday's eq. But even there, with Faraday's equation we think of the changing magnetic field as inducing the voltage in the loop, where in the model it seems the other way around, that is, the voltage increases...

Homework Statement Derive the transformations ##x \rightarrow \frac{x+vt}{\sqrt{1-v^{2}}}## and ##t \rightarrow \frac{t+vx}{\sqrt{1-v^{2}}}## in perturbation theory. Start with the Galilean transformation ##x \rightarrow x+vt##. Add a transformation ##t \rightarrow t + \delta t## and solve for...

Homework Statement The step I am trying to follow is detailed here where I am trying to get from equation 6.26: t=\int_{r_1}^{r}(1+\frac{2M}{r}+\frac{b^2V(r)}{2}+\frac{Mb^2V(r)}{r})dr to equation 6.30 t=\sqrt{r^2-r_1^2}+2Mln(\frac{r+\sqrt{r^2-r_1^2}}{r_1})+M(\frac{r-r_1}{r+r_1})^{1/2} Homework...

Why is relative speed taken to be symmetrical i.e. speed of one frame of reference from a second frame is equal to that of the second frame of frame refrence from the first frame

Homework Statement The first order ramp unit response is shown in the graph below. Determine: 1. The transfer function. 2. Plot the error function e(t) then determine its maximum magnitude and the time http://s24.postimg.org/cdbhqm80j/Capture.png Homework Equations G(s)=(1/T)/(S+1/T) ... G(s)...

For three years now i have been attempting to find some fundamental properties of gravity from which the three relativistic variables of GR, time dilation and the radial and tangent length contractions, could be determined without incorporating the EFE's. There is no rule or reason that i know...

Homework Statement [/B] I have this system below. It is the schematic of a linear accelerometer moving horizontally, where m is the total mass of the slide, b denotes the viscous damping, and k represents the spring constant. The relative position between the moving mass and the case is...

The commutation relations for the ##\mathfrak{so(n)}## Lie algebra is:##([A_{ij},A_{mn}])_{st} = -i(A_{j[m}\delta_{n]i}-A_{i[m}\delta_{n]j})_{st}##.where the generators ##(A_{ab})_{st}## of the ##\mathfrak{so(n)}## Lie algebra are given by:##(A_{ab})_{st} =...

The generators ##(A_{ab})_{st}## of the ##so(n)## Lie algebra are given by: ##(A_{ab})_{st} = -i(\delta_{as}\delta_{bt}-\delta_{at}\delta_{bs}) = -i\delta_{s[a}\delta_{b]t}##, where ##a,b## label the number of the generator, and ##s,t## label the matrix element. Now, I need to prove the...

Homework Statement A (spherical) rubbery balloon of 20 cm in diameter is filed with helium. The rubber balloon wall has a thickness of 0.05 cm and diffusivity of 0.1x10-10 cm2 /s for helium. When the balloon is left in the air at 25°C, helium leaks into the air by diffusion through the rubbery...

Homework Statement I'm trying to derive the vector identity: $$\nabla(\vec{A} \cdot \vec{B})$$Homework Equations $$ \nabla(\vec{A} \cdot \vec{B})=(\vec{B} \cdot \nabla) \vec{A} + ( \vec{A} \cdot \nabla ) \vec{B} + \vec{B} \times (\nabla \times \vec{A})+ \vec{A} \times ( \nabla \times \vec{B})$$...

Homework Statement For an upcoming test on 2D Motion, my Physics Teacher recommended that, instead of memorizing close to a dozen equations, he suggested we derive what we can from the main equations he showed us. So people in my class decided to split up deriving equations to bring them...

Homework Statement I need to derive the equation related to the Compton Effect from the equations for momentum and energy conservation. Homework Equations (1) Compton Effect: λ' -λ = h/me(1-cosθ) (2) Conservation of Momentum (x-direction): h/λ= (h/λ')cosθ+γumeucosΦ (3) Conservation of Momentum...

Homework Statement Integrate: Homework Equations The Attempt at a Solution I tried to get rid of the velocity in the numerator on the left side to use the relevant equation but to no avail. Any tricks on how i can integrate this? Also, this a small part of a larger mechanics problem...

Hello there, I'm reading a section of my textbook that is deriving the virial theorm from the hydrostatic equilibrium equation. In part of the derivation it states that $$-\int_0^M\frac{Gm(r)}{r}dm(r)=E_{GR}=-\frac{GmM}{r}$$ When I perform this integral I get the wrong answer. Here's my...

Homework Statement Consider heat flow in a long circular cylinder where the temperature depends only on t and on the distance r to the axis of the cylinder. Here r=\sqrt{x^2+y^2} is the cylindrical coordinate. From the three-dimensional heat equation derive the equation U_t=k(U_{rr}+2U_r/r)...

How does one derive the general form of the Riemann tensor components when it is defined with respect to the Levi-Civita connection? I assumed it was just a "plug-in and play" situation, however I end up with extra terms that don't agree with the form I've looked up in a book. In a general...

Homework Statement I still don't got the hang on Atwood Machines, and i don't know if I am wrong here or just overthinking it. But i got this one exercise where i am kind of stuck in two of the sub-exercises. So I am hoping there is someone here who could guide me in the right direction.Atwood...

Im currently trying to find out how my book took this drag equation (1/2 CApv^2P) and found the x and y component for accelration (x=(-pACv/2m)*sqrt (v(x)^2+v(y)^2)) &y=(-g-(-pACv/2m)*sqrt (v(x)^2+v(y)^2))

Homework Statement HI people, I was trying to derive the stefan-boltzman law from the planc's formula, I kind of got stuck with an integral Homework Equations $$ \int_{0}^{\infty} \frac{x^3}{e^x -1} dx $$ The Attempt at a Solution I tried simplifying it with $$ \int_{0}^{\infty} x^3...

Hello! My professors asked me why we don't usually consider the second Friedman equation. He told me that the solutions for the first always give a solution for the second. He told me that the first equation along with it's time derivative can imply the second equation. I have been trying the...

Homework Statement Please explain why we take the "integral of V^2" when deriving the root mean square of Voltage in alternating current? I do not understand why we integrate at all, instead of taking V as it is and squaring it. Also, when we DO integrate, why do we take the integral of "V^2"...

In Sean Carroll's Lecture Notes on General Relativity (Chapter 3, Page 60), in the chapter on Curvature, he derives the definition of the Christoffels Symbols by assuming the connection is metric compatible and torsion free. He then takes the covariant derivative of the metric and cycles through...

I'm trying to derive the law of reflection for Electromagnetic Waves and Optics. I'm using some lecture notes that my university provided. I'm confused as to why the two sine functions are changed to cosine functions as you don't do the same when you are deriving Snell's law. Refer to attached...

We have a circuit consisting of a charged capacitor and a resistor. First of all, we use Kirchhoff's loop rule to express this circuit in mathematical form. Now one teacher tells me Kirchhoff's loop rule yields iR+q/c=0. Another teacher tells me that the rule yields iR-q/c=0. Is there any...

Homework Statement Derive the Hamiltonian equation in terms of momentum and position ( p and r) for the given system whose lagrangian is stated as L=ř^2/(2w) - wr^2/2 Homework Equations L=ř^2/(2w) - wr^2/2 and H=př-L The Attempt at a Solution Notice here ř means first derivative of r. As i...

Hi, There is a cost of debt formula that goes c = ib(1-T), where c is the cost of issuing debt that firm incurs ( a percentage like interest) i is the interest earned by the investor, and T is the tax rate a firm pays. The key is that the interest rate alone is not really the cost of taking on...

Homework Statement As I've been going through examples in my textbook they are becoming increasingly lengthy to compute and thus I have resorted to using software to complete the task. For example when computing the series for ##\sin{(\ln{(1+x)})}##...

Hi! I have the following problem with some old lecture notes I recently had a look on. I have two different fermions (1 and 2) with masses m1 and m2 and the following Lagrangian (where the mass term for fermion 2 is dropped, because we are only interested in the dynamics of fermion 1) of the...

I am trying to derive Torricelli's equation, i.e. ##v_f^{2} = v_i^{2} + 2a\Delta x##, using calculus. There are two different ways I have seen. First we start with ##\displaystyle \frac {dv}{dt} = a##. Next, we multiply both sides by velocity, ##\displaystyle v\frac {dv}{dt} = a\frac {dx}{dt}...