Polar Definition and 1000 Threads

I am trying to find and solve the geodesics equation for polar coordinates. If I start by the definition of Christoffel symbols with the following expressions : $$de_{i}=w_{i}^{j}\,de_{j}=\Gamma_{ik}^{j}du^{k}\,de_{j}$$ with $$u^{k}$$ is the k-th component of polar coordinates ($$1$$ is for...

In my introduction to manifolds the following is stated: Polar coordinates (r, phi) cover the coordinate neighborhood (r > 0, 0 < phi < 2pi); one needs at least two such coordinate neighborhoods to cover R2. I do not understand why two are needed. Any point in R2 can be described by polar...

Homework Statement why x is p(cosθ)(sinφ) ? and y=p(sinθ)(cosφ)? z=p(cosφ) As we can see, φ is not the angle between p and z ... Homework EquationsThe Attempt at a Solution

Homework Statement can someone explain about the formula of the circled part? Why dA will become r(dr)(dθ)? Homework EquationsThe Attempt at a Solution A = pi(r^2) dA will become 2(pi)(r)(dr) ? why did 2(pi) didnt appear in the equation ?

Homework Statement Which of the following is the most polar molecule? ie. has the highest permanent electric dipole, CHCl3, SF6, SnCl4, BF3, CO2. CHCl3SF6SnCl4BF3CO2 Homework EquationsThe Attempt at a Solution I chose CHCl3 because I think it is the only molecule that is non-symmetrical so...

According to this video the length of basis is r. It grows as we further from the origin . Why?

Hello, Python,CFD and PF newbie here. I am using Spyder (Python 3.5) and I managed to plot my streamfunction in cartesian coordinates. I tried transforming and plotting in polar coordinates but I am not sure that what i have done is correct. I am not even sure what the plot should look like :/...

Homework Statement I need to find the work done by the force field: $$\vec{F}=(5x-8y\sqrt{x^2+y^2})\vec{i}+(4x+10y\sqrt{x^2+y^2})\vec{j}+z\vec{k}$$ moving a particle from a to b along a path given by: $$\vec{r}=\frac{1}{2}\cos(t)\vec{i}+\frac{1}{2}\sin(t)\vec{j}+4\arctan(t)\vec{k}$$ The Attempt...

Homework Statement "Areas of regions Make a sketch of the region and its bounding curves. Find the area of the region." "The region inside the curve ##r = \sqrt{cosθ}## and inside the circle ##r = \frac{\sqrt{2}}{2}##. Homework Equations ##A = \frac{1}{2}\int_α^β(f(θ)^2-g(θ)^2)dθ## Answer as...

I would like a discussion to quantify just how much mass is ejected at the poles (including the mass equivalence of the photons) when jets form. In quasars the black hole presumably reaches over a Billion solar masses, where the mass is proportionate to the mass of the galaxy and is also related...

Homework Statement "Slopes of tangent lines Find the slope of the line tangent to the following polar curves at the given points. At the points where the curve intersects the origin (when this occurs), find the equation of the tangent line in polar coordinates." ##7.##...

I am trying to evaluate \int\int xy dxdy over the region R that is defined by r=sin(2theta), from 0<theta<pi/2. I am struggling on where to begin with this. I have tried converting to polar coordinates but am not really getting anywhere. Any guidance would be really appreciated (Crying)

I heard (somebody told me and I also read from some paper) that a polar vector whose components are parameterized by the Dirac spinor \bar\psi\gamma^\mu\psi must be a timelike vector. Why is so? I think a general polar vector can either be timelike or spacelike, isn't it? Is that because a...

We know, that the infinitesimal area element in Cartesian coordinate system is ##dy~dx## and in Polar coordinate system, it is ##r~dr~d\theta##. This inifinitesimal area element is calculated by measuring the area of the region bounded by the lines ##x,~x+dx, ~y,~y+dy## (for polar coordinate...

Homework Statement Evaluate ∫∫D (3x + 4y 2 ) dA, where D = {(x, y) : y ≥ 0, 1 ≤ x 2 + y 2 ≤ 4} with the use of polar coordinates. Homework Equations The Attempt at a Solution I made a sketch of the circle. It's radius is = 1 and it's lowest point is at (0,0), highest at (0,2), leftmost point...

Homework Statement Using the cylindrical polar co ordinates ##(ℝ,θ,z)## calculate the gradient of ##f=ℝ sin θ + z^2## the textbook says that the scale factors are ## h1=1, h2=ℝ & h3=1## how did they arrive at this?[/B]Homework EquationsThe Attempt at a Solution ##h1=|∂f/∂ℝ|= sin θ...

Consider a central force. The central force is radial by definition, so ##\vec{F}=f(r) \hat{r}##. Therefore, by definition, the acceleration caused by the force, in the direction of ##\hat{\theta}## must be zero, ##\vec{a_{\theta}}=0##. In presence of central force angular momentum is...

H! I wonder how to solve: I=\int_{-\infty}^{\infty}e^{-u^2}\frac{1}{1+Cu} du I have solved: \int_{-\infty}^{\infty}e^{-u^2}du which equals \sqrt{\pi} and I solved it with polar coordinates and variable substitution. Thankful for help! Edison

Hi so I am a Civil engineering student with very little knowledge in circuits so I apologize if this question is redundant or common. I am trying to apply a current through a soil sample in order to consolidate it faster using Electro-Osmosis. Polarity Reversal should theoretically speed the...

I couldn't get equal graphs one plot 4 leafs the other 2

Homework Statement This is a physics olympiad problem; and I am still struggling with it. I will quote it here: " A particle moves along a horizontal track following the trajectory $$r=r_{0}e^{-k\theta}$$, where $$\theta$$ is the angle made by the position vector with the horizontal. Recall...

Studying the acceleration expressed in polar coordinates I came up with this doubt: is this frame to be considered inertial or non inertial? (\ddot r - r\dot{\varphi}^2)\hat{\mathbf r} + (2\dot r \dot\varphi+r\ddot{\varphi}) \hat{\boldsymbol{\varphi}} (1) I do not understand what is the...

Homework Statement Find the area in the first quadrant that is inside the circle ##r=100sin(\theta)## and outside the leminscate ##r^2=200cos(2\theta)##. I have graphed the region as I interpreted it below. The area I am trying to find is the non-shaded, white region. Homework Equations...

$$y=\sin\left({x}\right) $$ write in polar form This reduces to $$r=1$$ So that's not = plots Not sure why I can't get these simple equations

$y=x^3$ in polar form I got to this but it didn't plot ${x}^{3}$ $$r=\pm\sqrt{\frac{\sin\left({x}\right)}{\cos^3\left({x}\right)}}$$

Homework Statement B⃗ = -2.0ι^ + 3.0 j^. Find the polar coordinates r and theta. Homework Equations n/a The Attempt at a Solution r=sqrt((-2.0)^2+(3.0^2)) r = 3.6 theta = tan^-1(3/-2) = -56 degrees The answers seem to be wrong, can I get any guidance on this question please?

Homework Statement Consider Minkowski space in the usual Cartesian coordinates ##x^{\mu}=(t,x,y,z)##. The line element is ##ds^{2}=\eta_{\mu\nu}dx^{\mu}dx^{\nu}=-dt^{2}+dx^{2}+dy^{2}+dz^{2}## in these coordinates. Consider a new coordinate system ##x^{\mu'}## which differs from these...

Derive $y=3x$ as a polar equation and plot it. ?

Homework Statement A mass ##m## at the bottom of a circle of radius R moves back and forth with no friction and the follows the equation (where ##\alpha(t)## is small) ##\theta(t)=\frac{3\pi}{2}+\alpha(t)##. Find a differential equation using polar coordinates for ##\alpha(t)## which is linear...

Show that, in polar coordinates, the system is given by r′ = r(r^2 − 4) θ′ = 1x′1 = x1 − x2 − x1^3 x′2 = x1 + x2 − x2^3

I know that an arc length in polar coordinates can be computed by integrating $$\int ds$$ using the formula ##ds=\sqrt{\rho^2 + \frac{dr}{d\theta}^2}d\theta##. But, seeing that ##s=\rho\theta## and ##ds = \rho d\theta##, why is it wrong to calculate arc lengths with this expression for ##ds##?

Why does the polar jet stream flow counter-clockwise around the Earth (as viewed from the north pole)? It seems that since the air at the north end of the Ferrel Cell and the south end of the Polar Cell rises, the Coriolis effect would cause a circulation in the clockwise direction.

Homework Statement Homework EquationsThe Attempt at a Solution I have stared at this for hours and don't know where to start. I think I need to get r in terms of t but I don't really know how with the information given. I just need a good hint to get started.

Hi this isn't my homework, but it is taken from a worksheet for a Maths course(trying to refresh my rusty math), so I hope it fits in here. 1. Homework Statement two cylindrical polar vectors with same origin: P(2,55°,3); Q(4,25°,6) units in m Homework Equations a) Express in cartesian...

I am looking at this derivation of velocity in spherical polar coordinates and I am confused by the definition of r, theta and phi. http://www.usna.edu/Users/math/rmm/SphericalCoordinates.pdf I thought phi was the co latitude in the r,θ,∅ system and not the latitude. Of course the two are...

I need an android calculator app that will convert between rectangular and polar. I need these keys: ->R and ->P

I am looking to understand more about ##a=(\ddot{r}-r(\ddot{\theta})^2)\hat{r}+(r\ddot{\theta}+2\dot{r}\dot{\theta})\hat{\theta}## I understand the terms ##\ddot{r}## and ##r\ddot{\theta}## ,but why ##-r(\ddot{\theta})^2## has opposite direction to ##\hat{r}## and why ##2\dot{r}\dot{\theta}##...

My Intro to LA course has visited the ideas of polar decomposition and Jordan forms, but not gone into them in depth. I wouldn't say I understood them, but I'm aware of them, and could possibly solve some basic exercises involving them if all I had to do was apply formulas. My question is...

Homework Statement Find the volume of the solid lying inside both the sphere x^2 + y^2 + z^2 = 4a^2 and the cylinder x^2 + y^2 = 2ay above the xy plane. Homework Equations Polar coordinates: r^2 = x^2 + y^2 x = r\cos(\theta) y = r\sin(\theta) The Attempt at a Solution So I tried this...

Homework Statement arrange the following eluents in an increasing order of Rf of aspirin ethyl acetate, n-hexane, n-butanol, methanol Homework EquationsThe Attempt at a Solution my order is n-hexane < n-butanol < ethyl acetate < methanol but the order is wrong. i am thinking: aspirin is...

Homework Statement Express the quantity ∂2/∂x2+∂2/∂y2 in polar coordinates. Homework Equations x=ρcosφ y=ρsinφ ρ=sqrt(x2+y2) The Attempt at a Solution This is my first post, so I apologize for any weird looking equations, etc. I know that this is not a difficult problem, but I just cannot...

The given is determine a polar equation for circle satisfying the given conditions: the radius is $2$, and the polar coordinates for the center are: $\left(4,0\right)$ I got ${r}^{2}-8r\cos\left({\theta}\right)=-12$ But when I try to plot this to DESMOS get nutin.

How would I change the polarity of an object at a distance? Say there was a concrete wall (which does not conduct electricity). Say this wall was 100 feet away. How would I give that wall a positive charge from 100 feet away? High frequency radio waves?

Homework Statement Find all ##{\cal C}^1(\mathbb{R}_+^\star \times \mathbb{R},\mathbb{R}) ## solutions to the pde ##x\frac{\partial f}{\partial y} - y \frac{\partial f}{\partial x} = cf##, where ##c## is a constant. Use a polar change of variable. Homework Equations Trying to bring the...

Homework Statement Change the Cartesian integral into an equivalent polar integral and then evaluate. Homework Equations x=rcosθ y=rsinθ I have: ∫∫r2cosθ dr dθ The bounds for theta would be from π/4 to π/2, but what would the bounds for r be? I only need help figuring out the bounds, not...

Covert to polar $$y=3 x$$ I got... But it didn't plot on desmos... Can't show polar graph here? $$r\sin\left({\theta}\right)=3r\cos\left({\theta}\right)$$

Just couldn't find help with this anywhere but Using the desmos graphing calculator using the table feature I wanted to plot the points every $\frac{\pi}{12}$ $0<\theta<2\pi$ For $r=-2-3\sin(\theta)$ On a polar coordinate graph

Homework Statement I have the following complex numbers : -3,18 +4,19i I must put it in polar form. Homework Equations r=(a^2+b^2)^(1/2) cos x = a/r sin x = b/r The Attempt at a Solution I was able to find with cos x = a/r that the x = 127,20 But when I do it with sin x = b/r I obtain like...

Homework Statement I am currently trying to calculate the moment and products of inertia of a ring rotating about the x-axis at the moment the ring lies in the xy plane. The problem is that the notations I have from textbook are denoted for Cartesian coordinates. i.e. Ixx=∑i mi(yi2+zi2), and...

At time 1:11:20, Lenny introduces the metric for ordinary flat space in the hyperbolic version of polar coordinates? Is that what he is doing here? d(tau)^2 = ρ^2 dω^2 - dρ^2. He then goes on to say that this metric is the hyperbolic version of the same formula for Cartesian space, i. e...