deriving Definition and 1000 Threads

Problem: Starting from the gradient of a scalar function T(x,y,z) in cartesian coordinates find the formula for the gradient of T(s,ϕ,z) in cylindrical coordinates. Solution (so far): I know that the gradient is given by \nabla T = \frac{\partial T}{\partial x}\hat{x}+\frac{\partial...

Homework Statement An object has a position given by r-> = [2.0 m + (1.00 m/s)t] i + [3.0m−(5.00 m/s2)t2] j, where all quantities are in SI units. What is the magnitude of the acceleration of the object at time t = 2.00 s? Homework Equations All I am thinking here is that I can find...

I am given Z = f (x, y), where x= r cosθ and y=r sinθ I found ∂z/∂r = ∂z/∂x ∂x/∂r + ∂z/∂y ∂y/∂r = (cos θ) ∂z/∂x + (sin θ) ∂z/∂y and ∂z/∂θ = ∂z/∂x ∂x/∂θ + ∂z/∂y ∂y/∂θ= (-r sin θ) ∂z/∂x + (r cos θ) ∂z/∂y I need to show that ∂z/∂x = cos θ ∂z/∂r - 1/r * sin θ ∂z/∂θ and ∂z/∂y = sin...

Homework Statement Trying to derive the work-energy theorem, without manipulating differentials.Homework Equations a=\frac{dv}{dt} v=\frac{dx}{dt} W=\int F dx =ΔKE=\frac{1}{2}mvf^{2}-mvi^{2} The Attempt at a Solution F=ma \int F dx=m\inta dx =m\int\frac{dv}{dt}dx <-- I cannot continue...

Homework Statement I'm stuck at one of the derivations for relativistic energy. I've figured out every other single step, but I just can't wrap my head around this one: Prove that: {\frac{d}{dt}} {\frac {mu} {\sqrt{1-u^2/c^2}}} = {\frac {m {\frac{du} {dt}}} {(1-u^2/c^2)^{3/2}}}...

Homework Statement Wow LaTex fail... anyone know how i make this look like not ****? I had it looking all pretty on http://www.codecogs.com/latex/eqneditor.php and it gave me these codes as my latex markup but it didn't come out right... why do they look like source code and not the pretty...

This is an attempt by a novice to do something neat. Please feel free to correct me. I am trying to see if one can derive the Hamiltonian equations of motion from a simple statement of the conservation of energy for mechanical systems. My attempt: 1. For a system S with position q and a...

Hi, I think I need a sanity check, because I've been working on this for a while and I can't see what I'm doing wrong! According to several authors, including Sakurai (Modern QM eq 3.3.21), a general way to write an operator from SU(2) is...

Hi guys, So I'm starting to learn about magnetic fields and electrics fields, one of the equations we use is v= -L*di/dt ... I've been trying to figure out how it's derived, in my book it says: it starts off like this: 1. v=-dθ/dt (faraday's law) <- why is there no N(no. of turns)...

I am studying Bessel Function in my antenna theory book, it said: \pi j^n J_n(z)=\int_0^{\pi} \cos(n\phi)e^{+jz\cos\phi}d\phiI understand: J_m(z)=\frac{1}{2\pi}\int_0^{2\pi}e^{j(z\sin\phi-m\theta)} d\theta Can you show me how do I get to \pi j^m J_m(z)=\int_0^{\pi}...

Hello, There is this formula ∆t=Lv/c^2 I can't remember how it's called, but it is used to determine time difference between two clocks (one is at rest and the other is moving speed of v). L is the distance between two clocks. How do you derive this formula using special relativity...

Much like Simpson's Rule, a.k.a. the prismoidal method, improves upon the trapezoidal method by fitting parabolic arcs across known discrete points on some function $f(x)$ rather than line segments, Newton-Cotes formulas of order 1 and 2 fit cubic and quartic curves across points on the curve...

Can anyone give me the proof or point me to a link to derive this First Integral of Bessel's Function. J_n(x)=\frac{j^{-n}}{\pi}\int_0^{\pi}\cos(n\phi)e^{jx\cos \phi}d\phi I have been searching all over and can't find the derivation. In fact, other than some basic Bessel's identities that is...

I'm terrible at calculus and am trying an exercise to hopefully help me understand it better. I want to derive the equations of acceleration, velocity and position of a car with known power and mass. As the car's speed increases, the acceleration will decrease. force = mass/acceleration...

(My last https://www.physicsforums.com/showthread.php?p=4424810#post4424810 post did not get much attention so I try again without all these formulae. Think this will be more clear...) To derive the local field in a non-polar dielectric you assume a very small spherical cavity in which (since...

Hello PF, I have once simple (well, not so simple for me) question. I'm trying to derive an equation for the velocity of a falling body with accordance to terminal velocity. The equation incorporates drag proportional to the speed. m*dv/dt=mg-bv and mg/b=terminal velocity vt So the steps...

Homework Statement let f(a)=∫20|x(x-a) dx for 0≤a≤2 a)Find the function f(a) The Attempt at a Solution I think the function can be given by this but what I get does not seem to be the correct answer. ∫a0x(x-a)dx -∫2ax(x-a)dx The correct answer is supposed to be 1/3a3-2a+8\3

can anybody help me to derive eqn. (9.19) of Srednicki's QFT book?

Hello, I am trying to derive the equation for the B-field due to a moving charge. ~ Griffiths Chapter 10, equation 10.66. I have been trying to “do” the del cross A and simplify . Things get messy and I am uncertain on some of my vector operations. In searching the internet I find...

Hi Can somebody tell me the steps and assumptions made in deriving the equation to calculate the wind velocity around a low pressure area ? (see the attachment fro Kleppner & Kolenkow). I tried to derive like this : Coordinate system located on Earth's surface with i direction towards E, j...

(First post, hi everyone.) I'm reading Griffith's textbook on intro to quantum mech right now. After establishing the following equation $$\left\langle f(x) \right\rangle = \int f(x)p(x)\,dx$$ And thus $$\left\langle x \right\rangle = \int x|\Psi|^2\,dx$$ He goes on to find...

Homework Statement My professor wants to see how to derive the formula. Basically get from the first two lines in the bracket to the two lines that are boxed. Homework Equations I have attached the picture of the relevant equations

Homework Statement A projectile is fired from ground level at time t=0, at an angle of θ with respect to the horizontal. It has initial speed V0. Part A Find the time it takes the projectile to reach its maximum height. Express in terms of V0, θ, and g. Part B Find the time at...

\hbox { Bessel's equation of order p: }\;x^2y''+xy'+(x^2-p^2)y=0\;\hbox { and let}\;y=\sum_0^{\infty}C_nx^{n+r} \Rightarrow\; \left[\sum_0^{\infty}C_k(k+r)(k+r-1)x^k+\sum_0^{\infty}C_k(k+r)x^k+\sum_2^{\infty} C_{k-2}x^k-p^2\sum_0^{\infty}C_kx^k\right]x^r\;=\;0 \Rightarrow\...

Can anyone point me to a derivation of the navier stokes equations in polar? I don't see where the single derivative in theta terms are coming from in the first 2 components.

In this documentation from Nasa a procedure to get to what I guess is the gravitational acceleration according to the post-Newtonian expansion at the 1PN-level for the spherically symmetric case is found: http://descanso.jpl.nasa.gov/Monograph/series2/Descanso2_all.pdf The procedure is...

I was asked to formulate the equations governing the rotation of a body moving without any external moments acting about its centre of mass in terms of a coupled system of first order, nonlinear differential equations. I decided to go with the Euler equations, and I ended up with this...

Homework Statement The question asks one to derive the acceleration vector, $$\vec{a} = [\frac{d^2r}{dt^2} - r(\frac{d\Theta}{dt})^2]\vec{u}_r + [\frac{1}{r}\frac{d}{dt}(r^2\frac{d\Theta }{dt})]\vec{u}_\Theta$$ from the velocity vector. $$\vec{v} = \vec{u}_r\frac{dr}{dt} +...

Homework Statement Find derivative of abs (2x^3 + 8x^2 + 5x +1).Homework Equations The Attempt at a Solution A little confused on how the absolute value changes the method of deriving that equation. When I derive it normally, I get (6x^2+16x+5).

Homework Statement Hey all, I am having trouble following some of the notes that my professor posted with regards to waves inside a blackbody; here is what he posted: (the part in bold is what I am just not understanding) "Inside the blackbody box, we need for the position of the walls...

EDIT: Nevermind. I figured it out. The two expressions are, in fact, equal. An excerpt from a book at this link, http://webpages.sdsmt.edu/~ddixon/Departure_Fxns.pdf, states that the entropy departure function for any equation of state is equal to the following (Eqn. 4.4-28)...

Homework Statement I'm asked to start from Faradays Law & Ampere-Maxwell law then derive the equation for the magnetic field, B, in the form; del2B = 1/c2 * d2B/dt2 Homework Equations Faraday: curl E = -dB/dt A.M : curl B = ε0μ0 dE/dt The Attempt at a Solution taking curl of...

I have a derivation from a book that says Q = 2π Es / Ed Where Es is the energy stored in the resonant components. Dividing both by the period at resonance gives... Q = ωo Es / Pd This is where I'm stuck. The book says Es = 1/2 LI^2 at the instant that all of the energy is being stored in...

Hi, I'm trying to fill in the gaps in my notes - looking at a poroelastic model of tissue. We have the simple spherical model below. The centre sphere is where liquid is produced, then the two following spheres are brain tissue with different permeabilities, and the final sphere is an...

Homework Statement Homework Equations The Attempt at a Solution I've done all the parts easily. I just don't know how to derive the beat frequency fbeat. I cannot provide any workings because I don't know where to begin. I am not asking for an answer. I am asking for a...

Hello everybody. New here. Hope you are all doing well. I am a sophomore in college, studying physics and astronomy. I am in my first astrophysics class and struggling with how to approach problems. That being said, I need a little homework help if you can afford some time! 1. Starting with...

Homework Statement Is it possible to find the vector field line expression without the use of differential equations? Say I've sketched the field and found the shape to be parabolas, how would I find the general expression by just using the points I've been given?Homework Equations The Attempt...

Homework Statement Derive the formula to calculate the angle at which the road should be banked to prevent the car from skidding(Ignore force of friction). Homework Equations tan x = v^2/gr ----- answer mv^2/r = fcThe Attempt at a Solution I get how they derived the formula due to this website...

Is there a simple way of deriving Lorentz transformation? I don't find the typical derivations in textbook so convincing, which seems to use too many intuitive postulations...

Voltage across an inductor at any moment in time can be calculated as the inductance multiplied by the rate of change of current. How is this equation derived? I'm pretty sure it comes from Faraday law -emf = rate of change of magnetic flux but I cannot find the relationship. Thanks!

Hi i have been following Hobson in their attempt to derive the einstein tensor, I have split the varied action into three terms and want to factor out \delta(g^{\mu\nu}) terms. The Riemann tensor R_{\mu \nu} must be expanded to R^{\rho}_{\mu \nu p} and then contracted back to the original...

I am not really sure where to go from here, since T varies. I am guessing this means I am approaching the problem incorrectly, but in that case, I have no idea how to do it. Any help/guidance would be appreciated.

Hi. I am reading this chapter about dimensionless ratios and scaling law. and it says like this: \alphaF = \frac{Fp}{Fm} = \frac{ρp . Vp^2 . Lp^2}{ρm . Vm^2 . Lm^2} (1) From this, it is obvious one can write for these forces: Fp = C\frac{1}{2} ρp Vp^2 . Lp^2 (2)...

Homework Statement The total intensity I(T) radiated from a blackbody (at all wavelengths λ) is equal to the integral over all wavelengths, 0 < λ < ∞, of the Planck distribution (4.28). (a) By changing variables to x = hc/λkBT, show that ¡(T) has the form I(T) = σT4 where a is a constant...

Hi all, I was going through the derivation for the electromagnetic field of point charges by Griffith(Introduction to electrodynamics page 437). I'm missing minus sign somewhere: The book says that:\nabla(\vec{n}\cdot\vec{v})=\vec{a}(\vec{n}\cdot \nabla...

In K&K's text on mechanics, after they present the derivation of the work energy theorem: \frac{1}{2}mv^2-\frac{1}{2}mv_0^2=\int_x_0^x F(x) dx It is mentioned that since v=\frac{dx}{dt}, we could solve for \frac{dx}{dt} and integrate again to find x(t) I tried that with v_0=0 just to make...

Homework Statement I need to derive an expression for the displacement of light as a function of thickness of glass and the angles. I will post a screen shot of the formula to be derived but it can also be found here...

How would one derive the equation for (dP/dV)H? That is the partial of P over the partial of V, holding H constant. I've tried many different things, triple product rule, maxwell relationships, and nothing seems to work. I appreciate any advice.

Hi, I shall show (using Fourier transform) that the solution to \frac{\partial^2 u(x,t)}{\partial t^2} = \frac{\partial^2 u(x,t)}{\partial x^2}\\ u(x,0) = f(x) \\ u_t(x,0) = 0 is u(x,t) = (f(x+t) + f(x-t))/2 I got it almost: Taking the Fourier transform in the variable x...

Can moment of inertia be derived using just linear dynamics and calculus. Textbooks usually derive moment of inertia using energy equation and and analogy of 1/2mr^2w^2 with 1/2mv^2. I would like to know if it can be approached in a different manner using just linear dynamics.