Coordinates Definition and 1000 Threads

Homework Statement Use cylindrical coordinates to evaluate triple integral E (sqrt(x^2+y^2)dv where E is the solid that lies within the cylinder x^2+y^2 = 9, above the plane z=0, and below the plane z=5-y Homework EquationsThe Attempt at a Solution So i just need to know how to get the bounds...

Homework Statement A point charge +Q exists at the origin. Find \oint \vec{E} \cdot \vec{dl} around a circle of radius a centered around the origin. Homework EquationsThe Attempt at a Solution The solution provided is: \vec{E} = \hat{\rho}\frac{Q}{4\pi E_0a^2} \vec{dl}=\hat{\phi}\rho d\phi...

Greg Bernhardt submitted a new PF Insights post Rindler Motion in Special Relativity, Part 2: Rindler Coordinates Continue reading the Original PF Insights Post.

Suppose $\displaystyle f = e^{(x^2+y^2+z^2)^{3/2}}$. We want to find the integral of $f$ in the region $R = \left\{x \ge 0, y \ge 0, z \ge 0, x^2+y^2+z^2 \le 1\right\}$. Could someone tell me how we quickly determine that $R$ can be written as: $R = \left\{\theta \in [0, \pi/2], \phi \in [0...

Homework Statement a: In plane polar coordinates, find the scalar product of the vector (0,1) with itself. b: What would be the r, θ components of the unit vector in the θ direction? Homework Equations Scalar product of 2 vectors = AαgαβBβ The Attempt at a Solution For part a, I used the...

[Moderator's note: This thread is spun off from another thread since it was dealing with a more technical point that is out of scope for the previous thread. The quote that starts this post is from the previous thread.] I feel the same about transformations of Dirac matrices and Dirac field...

Homework Statement Homework EquationsThe Attempt at a Solution I am having a bit of trouble visualizing the vectors for these type of problems. The angles they give are very ambiguous and so I am not sure why they are there. For the 45 degree angle, how do i know that this is used for finding...

Hey people, this question was already asked here [https://www.physicsforums.com/threads/velocity-in-plane-polar-coordinates.795749/], but I just couldn't understand the answer given, so I was wondering if some of you could help me by explaining it again. I don't really get Equation (or...

Homework Statement -infinity < r > +infinity Which of the following are equations for the line y=m*x for m<0: a. theta = -arctan(m) b. theta = arctan(m) c. theta = arctan(-m) d. theta = arctan(m) + pi e. theta = arctan(m) - pi f. r = 1/(sin(theta - arctan(m))) 2. The attempt at a solution...

Homework Statement I am trying to solve the axisymmetric diffusion equation for vorticity by Fourier transformation. Homework Equations $$ \frac{\partial \omega}{\partial t} = \nu \Big( \frac{1}{r}\frac{\partial \omega}{\partial r} + \frac{\partial^2 \omega}{\partial r^2} \Big). $$ The...

Homework Statement I’m studying orthogonal curvilinear coordinates and practice calculating differential operators. However, I’ve run across an exercise where the coordinate system is only in 2D and I’m confused about how to proceed with the calculations. Homework Equations A point in the...

From "A Student's Guide to Langrangins and Hamiltonians", Patrick Hamill, Cambridge, 2017 edition. Apologies: since I do not know how to put dots above a variable in this box, I will put the dots as superscripts. Similarly for the limits in a sum. On page 6, "we denote the coordinates by qi...

I've been playing around a bit with the Kerr orbit program I wrote, and have been thinking about ways to set the initial conditions. One thing I'd like to be able to do is specify a launch from some event in terms that would be convenient for an observer at that event with some given...

Homework Statement Homework Equations x^2 + y^2 + z^2 = r^2 Conversion equations between the three coordinate systems The Attempt at a Solution I tried to solve this problem using spherical/cylindrical coordinates from the beginning, but that wouldn't work so I started with cartesian...

i don't know to using limit of r ?

$\tiny{up(alt) 244.14.4.8}\\$ $\textsf{Describe the given region in polar coordinates}\\$ $\textit{a. Find the region enclosed by the semicircle}$ \begin{align*}\displaystyle x^2+y^2&=2y\\ y &\ge 0\\ \color{red}{r^2}&=\color{red}{2 \, r\sin\theta}\\ \color{red}{r}&=\color{red}{2\sin\theta}...

Hi guys! For nuclear case, I need to write an Schrodinger equation in cylindrical coordinates with an total potential formed by Woods-Saxon potential, spin-orbit potential and the Coulomb potential. Schrodinger equation can be written in this form: $$[-\frac{\hbar^2}{2m}(\frac{\partial...

Is there a programmable telescope that will point to any spot on Earth from my location that I could simply plug in the latitude and longitude and it would point at the location anywhere on Earth. For instance, if I wanted it to point at the LHC (Large Hadron Collider), could I just plug in the...

Homework Statement The electric field in an xy plane produced by a positively chatged particle is 7.2(4x+3y)N/C at the point (3, 3)cm and 100x N/C at the poiint (2, 0)cm. Note, x and y used here are unit vectors. find the x and y co-ordinate of the charged particle what is the charge of the...

1) Firstly, in the context of a dot product with Einstein notation : $$\text{d}(\vec{V}\cdot\vec{n} )=\text{d}(v_{i}\dfrac{\text{d}y^{i}}{\text{d}s})$$ with ##\vec{n}## representing the cosine directions vectors, ##v_{i}## the covariant components of ##\vec{V}## vector, ##y^{i}## the...

Any point on the plane can be specified with an ##r## and a ##\theta##, where ##\mathbf{r} = r \hat{\mathbf{r}}(\theta)##. From this, my book derives ##\displaystyle \frac{d \mathbf{r}}{dt}## by making the substitution ##\hat{\mathbf{r}}(\theta) = \cos \theta \hat{\mathbf{i}} + \sin \theta...

Given the PDE $$f_t=\frac{1}{r^2}\partial_r(r^2 f_r),\\ f(t=0)=0\\ f_r(r=0)=0\\ f(r=1)=1.$$ We let ##R(r)## be the basis function, and is determined by separation of variables: ##f = R(r)T(t)##, which reduces the PDE in ##R## to satisfy $$\frac{1}{r^2 R}d_r(r^2R'(r)) = -\lambda^2:\lambda^2 \in...

Homework Statement The vlasov equation is (from !Introduction to Plasma Physics and Controlled Fusion! by Francis Chen): $$\frac{d}{dt}f + \vec{v} \cdot \nabla f + \vec{a} \cdot \nabla_v f = 0$$ Where $$\nabla_v$$ is the del operator in velocity space. I've read that $$\nabla_v =...

This might not be the usual kind of question posted here, but I am trying to solve a geocaching puzzle. The puzzle is called "An Irrational Location", and the only information provided is more or less the following: ~~~~~ No rational person should attempt to visit the posted coordinates Cache...

Homework Statement Problem 1: Use double integrals to find the volume of the solid obtained by the rotation of the region: ##\triangle = \left\{ (x, y, z) | x^2 \le z \le 6 - x, 0 \le x \le 2, y = 0 \right\} ## (edit) in the xz-plane about the z axis Homework Equations Volume = ##\int_a^b...

In Lagrangian mechanics, if the Lagrangian is not a function of one of the generalised coordinate, then it is called a cyclic coordinate. Why is it called such? What is the significance of the term 'cyclic'?

I have to present a topic "Good coordinates and degree of freedom" I know what are good coordinate and degree of freedom. but I will have to explain examples/question given below(from Liboff's text) I know the answer to all of them but I really do not know how to explain these how will I explain...

Hi, I'm getting into general relativity and am learning about tensors and coordinate transformations. My question is, how do you use the metric tensor in polar coordinates to find the distance between two points? Example I want to try is: Point A (1,1) or (sq root(2), 45) Point B (1,0) or...

(Forgive me if this is in the wrong spot) I understand how tensors transform. I can easily type a rule with the differentials of coordinates, say for strain. I also know that the moment of inertia is a tensor. But I cannot see how it transforms as does the standard rules of covariant...

Homework Statement I want to derive the expansion of ##\Phi(x)## in rectangular coordinates: $$ \Phi(\vec{x}) = \frac{1}{4\pi \epsilon_0} \bigg[ \frac{q}{r}+\frac{\vec{p}\cdot \vec{x}}{r^3}+\frac{1}{2}\sum_{i,j} Q_{ij} \frac{x_ix_j}{r^5}+\ldots\bigg]$$ Homework Equations $$\vec{p}= \int...

Hello All, I'm having a problem with my TI89 where it will output correctly if I input an equation of all one type (polar or rectangular), in whatever format I input the equation in. I'm hoping I just somehow messed up the modes when I reset my calculator! For example if I input (1∠2)...

Hey! :o Using polar coordinates I want to calculate $\iint_D \frac{1}{(x^2+y^2)^2}dxdy$, where $D$ is the space that is determined by the inequalities $x+y\geq 1$ and $x^2+y^2\leq 1$. We consider the function $T$ with $(x,y)=T(r,\theta)=(r\cos \theta, r\sin\theta)$. From the inequality...

< Mentor Note -- thread moved from the Homework physics forums to the technical math forums >[/color] Hello.I was reading recently barton's book.I reached the part corresponding to dirac-delta functions in spherical polar coordinates. he let :##(\theta,\phi)=\Omega## such that ##f(\mathbf...

How do you convert this to Spherical Components? Spherical Convention = (radial, azimuthal, polar) ##\vec r = |\vec r| * \cos{(\theta)} * \sin{(\phi)} * \hat x +|\vec r| * \sin{(\theta)} * \sin{(\phi)} * \hat y +|\vec r| * \cos{(\phi)} * \hat z## Is this correct? ##\vec r =\sqrt{(x^2 + y^2 +...

Homework Statement The first part of the question was to describe E the region within the sphere ##x^2 + y^2 + z^2 = 16## and above the paraboloid ##z=\frac{1}{6} (x^2+y^2)## using the three different coordinate systems. For cartesian, I found ##4* \int_{0}^{\sqrt{12}} \int_{0}^{12-x^2}...

Write interated integrals in spherical coordinates for the following region in the orders $dp \, d\theta \, d\phi$ and $d\theta \, dp \, d\phi$ Sketch the region of integration. Assume that $f$ is continuous on the region \begin{align*}\displaystyle...

Homework Statement 13.43 A child slides down the helical water slide AB. The description of motion in cylindrical coordinates is ##R=4m##, ##θ=ω^2t^2## and ##z=h[1-(\frac {ω^2t^2} {π})]##, where h=3m and ω=0.75rad/s. Compute the magnitudes of the velocity vector and acceleration vector when...

I need explanation of these formulas for polar coordinate system where position of an object is characterized by 2 vectors: r - from the origin to the object, and Φ - perpendicular to r, in the direction of rotation. https://drive.google.com/file/d/0ByKDaNybBn_eakJmS3dUVXVZUDA/view?usp=sharing...

Homework Statement 13.24 A particle travels along a plane curve. At a certain instant, the polar components of the velocity and acceleration are vR=90mm/s, vθ=60mm/s, aR=-50mm/s2, and aθ=20mm/s2. Determine the component of acceleration that is tangent to the path of the particle at this...

Homework Statement This is Pytels Dynamics 2nd edition problem 13.16 13.16. Pen P of the flatbed plotter traces the curve y=x3/80000, where x and y are measured in mm. When x=200mm, the speed of slider A is 60 mm/s. For this position, calculate (a) the speed of P; and (b) the normal component...

If the coordinates x = rsinθcosφ, y = rsinθsinφ, z = rcosθ represent a Sphere, then what does the coordinates x = rsinθcosφ, y = rsinθsinφ, z = rcosθsinφ represent? @fresh_42 @FactChecker @Infrared @WWGD

Homework Statement Pytel Dynamics Problem 13.4 13.4 The particle passespoint O at the speed of 2.4 m/s. Between O and B, the speed changes at the rate of 2.2√v m/s2, where v is the speed in m/s. Determine the magnitude of the acceleration when the particle is (a) just to the left of pont A...

Hi, on this page: https://en.wikipedia.org/wiki/Laplace_operator#Two_dimensions the Laplacian is given for polar coordinates, however this is only for the second order derivative, also described as \delta f . Can someone point me to how to represent the first-order Laplacian operator in polar...

Homework Statement question : find the value of \iint_D \frac{x}{(x^2 + y^2)}dxdy domain : 0≤x≤1,x2≤y≤x Homework Equations The Attempt at a Solution so here, i tried to draw it first and i got that the domain is region in first quadrant bounded by y=x2 and y=x and i decided to convert...

Homework Statement A sphere of radius 6 has a cylindrical hole of radius 3 drilled into it. What is the volume of the remaining solid. The Attempt at a Solution [/B] I am able to solve this using cylindrical coordinates but I'm having trouble when I try to solve it in spherical coordinates...

When discussing about generalized coordinates, Goldstein says the following: "All sorts of quantities may be impressed to serve as generalized coordinates. Thus, the amplitudes in a Fourier expansion of vector(rj) may be used as generalized coordinates, or we may find it convenient to employ...

Hi, everyone. I had an example from my book, but I wasn't sure how they got \dfrac{1}{2}cos\theta on step 7? It seems like once they combined the constants, they ended up with just cos2\theta. Although, they have a \dfrac{1}{2} in front. Can someone help me understand where that constant came...

A force F = -K(yi + xj) (K is a positive constant) acts on a particle moving in the x-y plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). What is the total work done by the force F on the...

Hey! :o We have a triangle $ABC$ with $A(a_1, a_2)$, $B(b_1, b_2)$ and $C(c_1,c_2)$. I want to show that the coordinates of the centroid S is $\left (\frac{1}{3}(a_1+b_1+c_1),\frac{1}{3}(a_2+b_2+c_2) \right )$. $S$ is the intersection point of the midpoints of AB, BC and CA. We have that...

To draw oblique coordinates with the coordinates measured perpendicular to each axis would be wrong, right? I saw it done in a fairly popular book. It's usually the case that I'm the one who is wrong, but I think the book is incorrectly treating minkowski diagrams. Look at these images from...