Polar Definition and 1000 Threads

Prepare a function m-file containing a function that converts polar coordinates in two-dimensional space to rectangular (Cartesian) coordinates. Include a suitable H1 line and some additional comment lines. The input will be 2 vectors, and the output will be 2 vectors. The length of each vector...

Hi all, I'm having some problems in grasping/properly understanding the usage of the del operator ( ##\nabla## ) in spherical co-ordinates, and I was wondering if someone could point me to some good resources on the subject, or take a bit of time to try to explain it to me. It just doesn't seem...

since HCl dissociates in H+ and Cl- like NaCl then why it is not ionic still?? tell except electronegativity diff?

Tried to post this in the resources forum but could not start a new thread. I can not find graphing software to plot data in polar coordinates. Anyone got links??

Sketch the curve with the given polar equation. θ = −pi/6? I know for certain that its a straight line that passes through the origin but what I'm not sure is if its like this \ or like this /

Sorry, the title's length didn't allow me to explain this better and I need it for a story that I'm writing, if you're so kind to help me. I've been trying it hard to solve it myself but I've been unable to. The problem looks simple but it isn't (for me): Please assume we have a space probe of...

This is a problem that has been bugging me all day. While working with the well-known dydx = rdrdθ, where r is a function of θ I divided both sides of the equation by dxdθ to get dy/dθ = r(dr/dx) For the left side, I use y = rsinθ and derive with respect to θ to get dy/dθ = sinθdr/dθ + rcosθ...

Hello folks! New to this forum, so hoping I'm not retreading old ground. The Pauli matrices are spin angular momentum operators in quantum mechanics and thus are axial vectors. But in Clifford algebra in three dimensions they are odd basis elements and thus polar vectors. Hestenes, Baylis, other...

Homework Statement The problem I'm stuck on is to come up with an equation which will model the path of the projectile in an xy-plane. We are given: r(t)={ [(v0cos(θ))t], [h+(v0sin(θ))t-(½)gt2] } v0=100 ft/s θ=60° h=4 ft so basically, r(t)={[100cos(60)t], [4+100sin(60)t-16t2]} Homework...

Homework Statement Given the polar curve r=e^(a*theta), a>0, find the curvature K and determine the limit of K as (a) theta approaches infinity and (b) as a approaches infinity. Homework Equations x=r*cos(theta) y=r*sin(theta) K=|x'y''-y'x''|/[(x')^2 + (y')^2]^(3/2) The Attempt at a Solution...

Homework Statement Which statement describe a polar molecule? a. The molecule has an uneven distribution of electron density [ans] b. The molecule has a linear polarity without charge c. The molecule has a tetrahedral geometry d. All of the above The Attempt at a Solution I would personally...

Hey, I know that one doesn't work with polar coordinates (t,r,θ,φ) because they don't behave well in the event horizon. But my problem is with raidal null curves, if we take ds2=0 and dφ, dθ = 0 so we have When, if I'm correct, the + sign determine that it's outgoing and the - infalling, so...

Homework Statement A particle moves with v=constant along the curve $$r = k(1+\cos \theta)$$Find ##\mathbf{a}## Homework Equations $$ \mathbf{r} = r\mathbf{e_r}$$ $$ \mathbf{v} = \frac{\partial}{\partial t}(r\mathbf{e_r}) $$ $$ \mathbf{a} = \frac{\partial \mathbf{v}}{\partial t} $$...

Homework Statement Evaluate r(hat and overdot), θ(hat and overdot), φ(hat and overdot) in terms of (θ , Φ) and the time derivatives of the two remaining spherical polar coordinates. Your results should depend on the spherical polar unit vectors. Homework Equations ∂/∂t= The Attempt at a...

If we expres cartesian cordinates in polar coordinates we get: x=r*cos(theta) y=r*sin(theta) let's differentiate those 2 eqs: dx= dr cos(theta) -r* d(theta) * sin(theta) dy=dr sin(theta) + r* d(theta) * cos(theta) why isn't dx*dy= r* dr* d(theta) ( like when taking the jacobian , or when...

Homework Statement A particle moves with constant speed ν around a circle of radius b, with the circle offset from the origin of coordinates by a distance b so that it is tangential to the y axis. Find the particle's velocity vector in polar coordinates. Homework Equations (dots for time...

The question is to find the area of a disk, r ≤ 2a×cos(θ) as in the figure "example-just an illustration" I used two methods, each gave different wrong answers - integrate 2a×cos(θ) dθ dr - from θ=0 to θ=π/2 and from r=2a to r=2a×cos(θ) ; then I simply multiplied the answer by 2. - integrate...

Polar to rectangular $$r=1-2 \sin\left({\theta}\right)$$ $${x}^{2}+{y}^{2}=\sqrt{{x}^{2}+{y}^{2 }}+2y$$ Is this an answer just hard to get $y=$

Hello :) I don't get this integral (Peskin & Schroeder P. 27 ) ##\int {{{{d^3}p} \over {{{\left( {2\pi } \right)}^3}}}{1 \over {{E_{\bf{p}}}}}{e^{i{\bf{p}} \cdot {\bf{r}}}}} = {{2\pi } \over {{{\left( {2\pi } \right)}^3}}}\int\limits_0^\infty {dp{{{p^2}} \over {2{E_{\bf{p}}}}}{{{e^{ipr}} -...

I have a 2D Gaussian: ## f(x,y) = e^{-[(x-x_o)^2 + (y-y_o)^2]/(2*{sigma}^2)}## which I converted into polar coordinates and got: ## g(r,θ) = e^{-[r^2 + r_o^2 - 2*r*r_o(cos(θ)cos(θ_o) + sin(θ)sin(θ_o))]/({2*{sigma}^2})} ## The proof for how this was done is in the attached file, and it would...

We are currently learning about enantiomers in organic chemistry class. So far, we've covered what makes an enantiomer, the concept of chirality, optical isomer naming systems, and the physical and chemical properties of enantiomers. One of the physical properties listed is that enantiomers...

Just started self teaching myself differential geometry and tried to find the christoffel symbols of the second kind for 2d polar coordinates. I am checking to see if I did everything correctly. With a line element of: therefore the metric should be: The christoffel symbols of the second kind...

I have an original function ##z_{xy}## that I converted into cylindrical coordinates, now denoted ##z_{rθ}##. I have shown the steps I took to get here in the image file posted named "Work." Now, I have taken that work and converted it into code to plot in Python. I plotted it in another piece...

Homework Statement Let R be the triangle defined by -xtanα≤y≤xtanα and x≤1 where α is an acute angle sketch the triangle and calculate ∫∫R (x2+y2)dA using polar coordinates hint: the substitution u=tanθ may help you evaluate the integral Homework EquationsThe Attempt at a Solution so the...

Hi, I was wondering if anyone could help with a vector question that I have. If I have a unit vector defined in cartesian co-ordinates as p= (0,1,0) how would I go about converting this vector to a cylindrical geometry. I understand that I will probably need to use p_r=sqrt(px^2+py^2) and...

$r=3-\cos\left({\theta}\right)$ ${r}^{2}=3r-r\cos\left({\theta}\right)$ ${x}^{2}+{y}^{2}=3r+x$ How you deal with 3r ?

Homework Statement The gradient, divergence and curl in spherical polar coordinates r, ∅, Ψ are nablaΨ = ∂Φ/∂r * er + ∂Φ/∂∅ * e∅ 1/r + ∂Φ/∂Ψ * eΨ * 1/(r*sin(∅)) nabla * a = 1/r * ∂/∂r(r2*ar) + 1/(r*sin(∅)*∂/∂∅[sin(∅)a∅] + 1/r*sin(∅) * ∂aΨ/∂Ψ nabla x a = |er r*e∅ r*sin(∅)*eΨ | |∂/∂r ∂/∂∅...

Homework Statement I have a field w=wφ(r,θ)eφ^ (e^ is supposed to be 'e hat', a unit vector) Find wφ(r,θ) given the curl is zero and find a potential for w. Homework Equations I can't type the matrix for curl in curvilinear, don't even know where to start! I've been given it in the form...

$2\sin\left({\theta}\right)-3\cos\left({\theta}\right)$ Convert to rectangular coordinates I'm clueless?

Like asteroid clusters or any kind of what-not thought to be part of our solar system?

I'm on a tablet and having trouble with the math symbols so, for clarity, ∫[a,b] xdx is the integral from a to b of x with respect to x, and f(x) |[a,b] is a function of x evaluated from a to b. Problem: ∫[-1,1]∫[-√(1 - y2),√(1 - y2)] ln(x2 + y2 + 1) Relevent Equations: x2 + y2 = r2 ∫udv =...

Homework Statement [/B] Determine the rectangular and polar radii of gyration of the shaded area about the axes shown. Homework Equations dIx = y2dA Ix = ∫y2dA dA = ydx A = ∫(dA The Attempt at a Solution dIx = y2dA =(x6/16) *(x3/4) dx =(x9/64)dx Ix =(integrating from 1 to 2) ∫dIx =...

Homework Statement ∫∫dydx Where the region Ω: 1/2≤x≤1 0 ≤ y ≤ sqrt(1-x^2) Homework EquationsThe Attempt at a Solution The question asked to solve the integral using polar coordinates. The problem I have is getting r in terms of θ. I solved the integral in rectangular ordinates using a trig...

Hello Excuse me, but how do I sketch the phasor of a voltage that it's V=5cos(10t+30degrees) and how the V=5sin(10t+30degrees) ? I know that these can be converted as the R<angle polar form, with R being the Vmax, ie the 5, and the angle the phase. But what doesn't it matter if I have cos or...

I want to solve a Laplace PDE in a polar coordinate system with finite difference method. and the boundary conditions: Here that I found in the internet: and the analytical result is: The question is how its works? Can I give an example or itd?Thanks

hi, i'm a newbie... i have this problem: i have a sphere with known and constant R (obvious), i have two point with spherical coordinates P1=(R,p_1,t_1) and P0=(R, p_0, t_0) p_x = phi x = latitude x t_x = theta x =longitude x the distance between point is D=...

Homework Statement A projectile is launched from a mountain at a given angle and velocity (which is large). Using polar coordinates find the position of the particle at time t. I'm ignoring drag (for now). Homework Equations I tried using the polar kinematic equations...

I've been trying to solve this question all day. If somebody could point me in the right direction I would really appreciate it! (ii) A particle’s motion is described by the following position vector r(t) = 4txˆ + (10t − t)ˆy Determine the polar coordinate unit vectors ˆr and ˆθ for r. [4]...

Homework Statement The region between sphere x^2+y^2+z^2=3 and the upper sheet of the hyperboloid z^2=x^2+y2+1. Homework EquationsThe Attempt at a Solution Curve of intersection: We set the two equations equal to each other and find x^2+y^2=1, a circle of radius 1 is the curve of...

I'm in the middle of the Great Courses Multivariable Calculus course. A double integral example involves a quarter circle, in the first quadrant, of radius 2. In Cartesian coordinates, the integrand is y dx dy and the outer integral goes from 0 to 2 and the inner from 0 to sqrt(4-y^2). In...

Homework Statement Under certain conditions the interaction between a "polar" molecule such as HCl located at the origin and an ion located along the x-axis can be described by a potential energy U=−bhttps://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/144/char3D.pngx^2, where b is a...

The magnitude of the parallel component of the time derivative of a vector ##\vec{A}## is given by: $$|\frac{d\vec{A}_{\parallel}}{dt}| = |\frac{dA}{dt}|$$ Where ##A## is the magnitude of the vector. Can we write the actual derivative in vector form as ##\frac{dA}{dt} \hat{A}##? Notice how I...

The position of a point in cartesian coordinates is given by: $$\vec{r} = x \hat{\imath} + y \hat{\jmath}$$ In polar coordinates, it is given by: $$\vec{r} = r \hat{r}$$ Now, ##x = r \cos{θ}## and ##y = r \sin{θ}## assuming ##θ## is measured counterclockwise from the ##x##-axis. Equating the two...

Homework Statement I am trying to convert the following vector at (1, 1, 0) to cylindrical polar coordinates, and show that in both forms it has the same direction and magnitude: ##4xy\hat{x}+2x^2\hat{y}+3z^2\hat{z}## Homework Equations ##\rho^2=x^2+y^2## ##tan \phi = \frac{y}{x}## ##z=z##...

Homework Statement Write the chain rule for the following composition using a tree diagram: z =g(x,y) where x=x(r,theta) and y=y(r,theta). Write formulas for the partial derivatives dz/dr and dz/dtheta. Use them to answer: Find first partial derivatives of the function z=e^x+yx^2, in polar...

Homework Statement Attached. Homework Equations The Attempt at a Solution Hi, Ok, so for the first part of this question it asks to evaluate the integral of the dot product between A and dS. The magnitude of dS is as shown above, and it is in the radial direction in spherical polar...

It it bad practice to consider values of ##r## that are greater than or equal to zero, while ignoring negative values? Do I lose any information in my analysis of motion? I understand what values of ##r < 0## represent, and I'm willing to use them in a pure mathematics context. In classical...

For a dipole, if there is point subtending an angle ##\theta## at the centre of dipole and at a distance ##r## from centre of dipole, then the electric field at that point can be broken into 2 components. One along the line joining the point and centre of dipole and point given by...

Homework Statement Given that: theta_dot = 6 rad/sec m_A = 0.8kg u_k = 0.40 The problem also mentions that movement is at a constant angular rate so I think that means: r_doubleDot = 0 theta_doubleDot = 0 Lastly, at an instant: r_dot = 800mm/sec = 0.8m/sec 2. Homework Equations...

Homework Statement Express f(x,y) = \frac{1}{\sqrt{x^{2} + y^{2}}}\frac{y}{\sqrt{x^{2} + y^{2}}}e^{-2\sqrt{x^2 + y^2}} in terms of the polar coordinates \rho and \phi and then evaluate the integral of f(x,y) over a circle of radius 1 centered at the origin. Homework Equations y = \rho...