Cartesian coordinates Definition and 91 Threads

Homework Statement The following equation describes a surface in spherical coordinates. θ =pi/4 Write the equation in the cartesian coordinates? that is, (r,θ,Ø) to (x,y,z) Homework Equations x=rsinθcosØ y=rsinθsinØ z=rcosθ r=sqrt(x^2+y^2+z^2) θ=cos^-1(z/r) Ø=tan^-1(y/x) The...

Give a parametric representation of the following surfaces in terms of the given parameter variables: a) The first octant portion of the sphere (x^2) + (y^2) + (z^2) = 16 in terms of the spherical variables theta and phi. b)The graph of the function z = (x^3) - sqrt(y) in terms of the...

Homework Statement Consider a velocity field where the radial and tangenetial components of velocity are V_r=0 and V_theta=cr, respectively, where c is a constant. Obtain the equations of the streamlines. Homework Equations x=rcos(theta) y=rsin(theta) The Attempt at a Solution I...

Homework Statement The Carteian coordinates of a point on a circle with its center at the origin are [0.40, 0.30]. What is the arc length measured counterclockwise on the circle from the positive x-axis to this point? Homework Equations The Attempt at a Solution Wouldn't they be...

Why is \sqrt{9+36} = 3\sqrt{5} and not 6.708 ? I wasnt interested in maths at school but now I'm trying to self teach, so pardon my ignorance. Edit: Ok i feel foolish now, no need to correct me as I've just worked out i WAS correct. I'm still unsure as to why it would be shown...

Homework Statement Question 3 (a)A long metal cylinder of radius a has the z-axis as its axis of symmetry.The cylinder carries a steady current of uniform current density J = Jzez. Derive an expression for the magnetic field at distance r from the axis,where r<a. By resolving the...

Hi, Everyone: I just read recently a comment to the effect that Descartes never intented his use of coordinates in his layout of analytic geometry to be used globally; there was also a follow-up comment about " no one really using any coordinates in a global way. Does anyone...

Hi there, a few days ago I derived the probably well-know expression for the magnetic field of a current loop including elliptic integrals of the first and second kind (it can be seen here http://plasmalab.pbworks.com/f/bfield.pdf" ). As I'd like to rotate and shift the position of the...

[SOLVED] Electric field in cartesian coordinates Homework Statement Suppose the electric potential is V(r) = C1 /r + C2 cosθ /r^2 where (r, θ, φ) are the spherical polar coordinates for points in three dimensions. [Data: C1 = 4.3 Vm ; C2 = 1.6 Vm^2 ] (A) Determine the electric...

Homework Statement Write the following polar equation in Cartesian coordinates: r= 2/(3cos(theta)-9sin(theta)) Homework Equations r = (x^2 + y^2) ^.5 x=rcos theta y=rsin theta sin^2(x)+cos^2(x) = 1 The Attempt at a Solution I'm stuck on how to do this. Any push in the right...

We learned about cartesian coordinates briefly in class and i didnt completely understand them. I am not looking for an answer but rather the process on how to get to an answer in cartesian coordinates, for instance, in this example: A point on a polar coordinate system is located at r=2.0...

Homework Statement The vector V is given by V = (5.0x-12.0y )m. What is W such that V + W = -5|V|x? Homework Equations |v| = (vx2 + vy2)1/2 The Attempt at a Solution I was unsure of what I did to subtract vector v- I know the negative vector has the same magnitude but opposite...

Homework Statement Hi there. Well, I have the next exercise, which I've solved, but I don't know if the solution I got is the right one. It says Given the next region on spheric coordinates find the expression for it in rectangular coordinates, and plot...

Homework Statement Write the vectors B,D, and F in the figure in Cartesian form, with unit vectors. (See attachments) Homework Equations ax = a cos theta ay = a sin theta where a = magnitude of vector a, and theta = the angle vector a makes with the positive direction of the x axis...

Homework Statement Hi there. Hi have in cylindrical coordinates that \theta=\displaystyle\frac{\pi}{3}, and I must make the graph, and take it into cartesian coordinates. How should I do? I've tried this way: \begin{Bmatrix}x=r\cos\displaystyle\frac{\pi}{3}\\y=r\sin\displaystyle\frac{\pi}{3}...

Has to convert B6-1 into B6-2 Source Transport Phenomenon 2nd ed -

Dear all, How can I derive the volume of a spherical cap by integration and using the Cartesian coordinate system. The sphere is located at the (0,0,0) coordinates and its radius is set to r. The height of the cap is also set to (r-h). I googled a lot but I couldn't find it. I would...

Is it possible to do general relativity but avoid the difficult mathematics of generalized coordinates, tensors, and computing the metric of a space-time manifold by using ordinary cartesian coordinates in a 5 dimensional space? We can picture a curved 4 dimensional spacetime as being...

Homework Statement Find the gradient of 3r^2 in spherical coordinates, then do it in Cartesian coordinates Homework Equations \nabla f=\hat r \frac{\partial f}{\partial r} + \hat \theta \frac{1}{r} \frac{\partial f}{\partial \theta}+ \hat \phi \frac{1}{r\sin \theta}\frac{\partial...

[b]1. Was wondering if anyone could help me confirm the polar limits of integration for the below double integral problem. The question itself is straight forward in cartesian coordinates, but in polar form, I'm a bit suspect of my theta limits after having sketched the it out. any help much...

Homework Statement Solid horn obtained by rotating the points {[x=0], [0 \leq y \leq 4], [0 \leqz \leq \frac{1}{8}y^{2}] } circles around y-axis of radius \frac{1}{8}y^2. Set up the integral dzdxdy.Homework Equations Cartesian coordinates.The Attempt at a Solution I don't understand how the...

So I wonder why the gradient in coordniates other than cartesian ones bears coefficients. Let's take spherical coordinates for example. We have (Source) - Sorry if image doesn't work - too lazy to get the TeX right. From what I know, I don't see anything that raises cartesian coordinates...

I've found a fairly concise review of the Kerr metric at http://www.physics.mcmaster.ca/phys3a03/The%20Kerr%20Metric.ppt The Kerr Metric for Rotating, Electrically Neutral Black Holes: The Most Common Case of Black Hole Geometry. Ben Criger and Chad Daley. On slide 6 they give the usual...

Homework Statement Use a triple integral to find the volume of the solid enclosed by the paraboloid x=y^2+z^2 and the plane x=16 Note: The triple integral must be performed in Cartesian coordinates. Homework EquationsThe Attempt at a Solution I calculated the answer numerically using...

Hello. Is there some easy way to convert screen coordinates (origin at the top left corner) to Cartesian coordinates?

Homework Statement Convert F into cartesian coordinates from spherical F = -4*theta*e_r + 1e_phi r(t) = 2, theta(t) = 4t, phi(t) = pi / 2 Homework Equations x = rsin(theta)cos(phi) y = rsin(theta)sin(phi) z = rcos(phi) The Attempt at a Solution Where I'm having problem is converting F into...

Homework Statement Convert the following cylindrical coordinate vector to a Cartesian vector: \overrightarrow{A}\,=\,\rho\,z\,sin\,\phi\,\hat{\rho}\,+\,3\,\rho\,cos\,\phi\,\hat{\phi}\,+\,\rho\,cos\,\phi\,sin\,\phi\,\hat{z} Homework Equations...

How do you draw an Cartesian 3D-axis-system? The Y-axis seems to have some perspective; what's the position of the observer? What's the 'way' of placement, and why? All 'links' are welcome. Dank u.

[SOLVED] Latitude Longitude -&gt; Polar Form -&gt; Cartesian Coordinates Homework Statement I need to convert 46 Degrees North 80 Degrees west into Cartesian coordinates, based on the assumption that the Earth is a sphere (althought it's not). Homework Equations...

Homework Statement The polar coordinates of a point are r=6.00 m and theta 250. What are the Cartesian coordinates? X=? Y=? Homework Equations Cos=adj./hyp. sin=opp./hyp The Attempt at a Solution Would I just need to calculate the cos and sin? That is, I would just do sin...

Homework Statement Use separation of variables in cartesian coordinates to solve the infinite cubical well (or "particle in a box"): V(x,y,z) = \{^{0, if x, y, z are all between 0 and a;}_{\infty , otherwise.} Homework Equations Well, I've been trying to use \frac{1}{2}mv^{2} + V =...

What is the sequence described by the counts of integer Cartesian coordinates (x, y) within circles of successive whole number radii centered at the origin?

I don't know where have I gone wrong... I converted Cartesian coordinates to polar coordinates: \frac{\partial^2\Psi}{\partial x^2} +\frac{\partial^2\Psi}{\partial y^2}= \frac{1}{2}(\frac{\partial^2}{\partial x^2}+\frac{\partial^2 }{\partial y^2})\Psi^2 - \Psi(\frac{\partial^2}{\partial...

With the success of my effort to write the orbits of the Schwarzschild metric in "Cartesian" coordinates, (see https://www.physicsforums.com/showthread.php?t=126996 ) it is now time to compute the orbits for Painleve coordinates. When I'm done, I will have an applet that allows the computation...

My Java applet gravity simulator http://www.gaugegravity.com/testapplet/SweetGravity.html draws beautiful orbits, however the GR simulation is very badly broken as one can tell when comparing it with Newton at long distances. The source code is at...

How to get the Cartesian coordinates of an atom? Dear friends, Such a question confused me when reading!:confused: "xi,yi and zi are the Cartesian coordinates of the ith atom" How to get the coordinate of an atom? For example: carbon, oxygen? I think the atom is only a dot! What's the way...

This section I don't understand at all... but the problem is What is the torque tau_B due to force F_vec about the point B? (B is the point at Cartesian coordinates (0, b), located a distance b from the origin along the y axis.) Express the torque about point B in terms of F, theta, phi, pi...

Are Cartesian coordinates two or three dimensional?

I've no idea what to do with this, the examples didn't have anything of this style: The point A has coordinates (3,0,0), the point B has coordinates, (0,3,0), the point C has coordinates (0,0,7). Find, to 0.1 degrees, the sizes of the angle between the planes OAB and ABC, where O is the...

I am struggeling with the following problem: give the x,y,z coordinates from the following ball points/vectors 1. (r, theta, phi) = (sqrt3, 3/4pi, 3/4pi) 2. (r, theta, phi) = (1, 1/6pi, 1 1/6pi) the sollutions I found in my reader are as followed: 1. (x, y, z) = (-1/2 sqrt3, 1/2...

Hi. I was just wondering if anyone could help me with a formula to solve the following problem. I have two locations (L1 and L2), which I know the cartesian coordinates of, situated in a three dimensional space. I also have a distance (D) which I also know the value of. D is not the...