Polar Definition and 1000 Threads

Apparently one can deduce the form of divergence in polar (and spherical) coördinates using the theorem of Gauss and Ostrogradsky, namely that the volume integral over the divergence is equal to the flux integral over the surface. I can't see a way to do that, do you?

Homework Statement Hey am studing for my up coming exam and i am having trouble with transforming double intrgral to polar coordinates i have no idea where to start or anything so can someone explain it to me Homework Equations this is example \oint^{\infty}_{0}\oint^{\infty}_{0}...

Hello everybody, I am having trouble doing this polar double integral. The problem says.. Find the area of the region.. \frac{1}{2}y^2 \leq x \leq 2y 0 \leq y \leq 8 It is hard for me to come up with the limits of integration. Checking the answer would be easy because I can...

I got this equation 5<0° = -14.14<-45° + 2.24<116.6° I2 And i solved I2 this way I2 = -14.14<-45° / 2.24<116.6° I2 = 8<150.29° I want to know complex numbers is the same way as normal math or not thanks in advance

Hi guys! I was reviewing some basic stuff in Special Relativity, specifically the part where it can be proven that a straight line connecting two events is the path that maximizes the interval between these two events. The proof is easy using the metric with cartesian coordinates ds^2 =...

Can polar co-ordinate system only be defined in a "background" Cartesian co-ordinate system? What I'm confused about is this: the definition of the polar unit vectors or the polar basis is in terms of the parameter theta. Now, before we go about defining our basis we need to define this theta...

The electronegativity of Oxygen is higher than that of H, thus the electrons tend to stay a little more on the oxygens electron orbitals, right?

Solving a PDE with Polar coordinates yu_x-xu_y=0 x=r\cos{\theta} \ \mbox{and} \ y=r\sin{\theta} u(r,\theta) Does u_x\Rightarrow u_r \ \mbox{or} \ u_{\theta} \ \mbox{and why?} Thanks.

Hello, I've just found a book which mentions the formula for calculating the volume of a rotated polar function: \int_{\theta_1}^{\theta_2} \frac{2}{3} \pi r^3 sin(\theta) d\theta How does one calculate this? In an https://www.physicsforums.com/showthread.php?t=457896", I calculated that the...

Hello, I was wondering if anyone could help me with deriving the volume created by the rotation of a polar equation around the initial line. So, I thought about adding the surface area of cones (multiplied by d\theta) if each cone the triangle created with s-length of f(\theta) and r-length...

Homework Statement Given the equation r²=25sin2Θ Asked to find symmetry with respect to line Θ = pi/2 Homework Equations w.r.t. Θ = pi/2: (r,Θ) - (r, pi-Θ) and (r, Θ) - (-r,-Θ) The Attempt at a Solution For the first case, I plugged in (pi-Θ) for Θ, but I'm confused about what to do...

Homework Statement \int_{y=-infinity}^{infinity} \int_{x=-infinity}^{infinity} (x^4+y^4)/(1+x^2+y^2)^4 dx dy Homework Equations i'm not sure what the new limits are after the transformation to polar coordinates and how to solve the integral. The Attempt at a Solution i have my...

Homework Statement This is another problem my teacher game me. Given the Polar function r=6*sin(t/2) where the variable t is the angle theta in radians, and that t is between 0 and 2*Pi inclusive. Find the distance around the perimeter of the graph. Hint: this is arc length , round to the...

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...

Homework Statement Find the area of the infinitismal region expressed in polar coordinates as lying between r and r+dr and between theta and theta+dtheta Homework Equations A= [integral] (1/2)r^2 d[theta] The Attempt at a Solution To be honest I solved many of this kind of...

Homework Statement A plate with constant mass per unit area \rho is bounded by the curve (x^{2} +y^{2})^{2} = 9(x^{2} - y^{2}) . Find its moment of inertia about the x-axis. Homework Equations The Attempt at a Solution Okay well first I plugged in...

Alright, so I'm having a problem converting to polar co-ordinates Never been confused by polar before :(I'm trying to convert the domain of an integral to polar co-ordinates The domain would be something like D:{(x,y)| 1<x<2 , 0<y<(2x-x2) 1/2} First I recognize that y=(2x-x2) 1/2 is the...

Homework Statement Bounded by the paraboloid z = 4 + 2x2 + 2y2 and the plane z = 10 in the first octant. Homework Equations The Attempt at a Solution Plugging in 10 for z I got 3=x2+y2. From this, I set 0\leqr\leq3\sqrt{}. I wasn't sure what to do with the first octant, but I...

Homework Statement Determine the Jacobian determinant for "polar" coordinates and use that to compute the intergral . . . Blah blah blah that's not the point. Homework Equations (x,y) maps by T to (r, theta) or (theta, r) detT = jacobian The Attempt at a Solution Anyways, first I...

I was overlooking a problem that my teacher solved and i can't understand a step see took i was wondering if someone you tell me how she got from this step Double integral rcos(o)(rsino)rto this Double integral (r/2)^3(2sinocoso)

Homework Statement 6...y ∫...∫ x dx dy 0 ...0 The Attempt at a Solution for reference: π=pi 6...y ∫...∫ x dx dy 0 ...0 y=6=x=6. rcosΘ=6 r=6/cosΘ goes to π/2 6secΘ ∫ ...∫... r cosΘ r dr dΘ π/4...0 π/2.....r=6secΘ ∫ ... [((r^3)/3)cosΘ] dΘ π/4......r=0 π/2...

r = cos(theta) in polar coordinates?? Hullo everyone! Hows it going? I am confused with how to interpret the graph of r = cos(theta) in polar coordinates. I tried graphing it manually. and this is how I interpreted it: r(0) = cos(0) = 1 r(pi/2) = 0 r(-pi) = -1 r(3pi/2) = 0 r(2pi)...

This question may be something of a dumb one. I feel I should know this, but well, I don't. I'm being asked to find the perimeter inside of the curve r=15sin(theta) and outside of r = 1 Setting up the equation I can do. If it were just an indefinite integral, this would be cake. My...

Homework Statement Find the length of the polar curve r = psin3(\theta/3) Hint: The period of the curve is 3\piHomework Equations L = \intsqrt(f(\theta)2 + f'(\theta)2)d\thetaThe Attempt at a Solution I know from the hint that 0\leq\theta\geq3\pi The only problem I have is how do I start this...

Water molecules are polarized, so why don't the molecules in a glass of water simply line up with opposite + and - ends and come to a halt?

hi i need a affirm of curvature in polar coordinates. i need now please

Howdy everyone, I'm on a quest for something that is proving a bit elusive at the moment: a Cartesian to polar transform (along with its inverse) for \mathbb{R}^4. I'm well aware of how to derive the transform for both \mathbb{R}^2 and \mathbb{R}^3, as it is just a matter of looking at the...

Homework Statement Okay here's the problem: Consider the region R interior to a circle(of r =2) and exterior to a circle(r=1). 1.Using cartesian coords and double integral, calc the area of annulus. 2. repeat calculation above but using double integral with polar coords The...

Homework Statement Well the problem is a electromagnetism problem: I need to find the charge density. Given E= kr^3 r^ Homework Equations formula is gradient E=p/e0 The Attempt at a Solution They got the gradient of E to be 1/r^2 (d/dr) (r^2 Er) i have no idea how they did...

Homework Statement Find the area of the lemniscate r2=6cos(2w) located to the right of the line r=3/2sec(w). Homework Equations Area of a polar region is the integral from a to b (in this case a and b are where the curve intersects the line, I believe) of 1/2*r2d(w). The Attempt at...

Homework Statement Convert the following Cartesian equation to polar form. x^2/9 + y^2/4 = 1 Homework Equations r*cos(t)=x r*sin(t)=y r=Sqrt(x^2 + y^2) y/x = Arctan(t) The Attempt at a Solution I get ugly looking things like r^2(cos^2(t)/9 + sin^2(t)/4) = 1 but being a simple ellipse (edit...

Homework Statement Convert -2^i to polar and rectangular form Homework Equations mag(a+ib)=sqrt(a^2+b^2) exp(i*angle)=cos(angle)+i*sin(angle) The Attempt at a Solution im not sure how to get the polar (or rectangular form) of -2^i. i know the answer is exp(-2.448rad)... i just don't know the...

Homework Statement Show that the solution x(t) = Ge^(iwt), where G is in general complex, can be written in the form x(t) = Dcos(wt - \delta). D(w) and \delta(w) are real functions of w. Homework Equations z = Ae^(i\phi) The Attempt at a Solution So I know I should start by...

in this situation where apollo 13 is reentering the atmosphere, how would you determine what theta is in the polar coordinate system for velocity? [PLAIN]http://img37.imageshack.us/img37/7366/shuttlek.jpg Wouldn't the angle gamma be equal to theta since gamma is equal to the angle of the...

how to expand grad f * (p-p_0) in spherical polar coordinates in spherical polar coordinates: \nabla f = \frac{\partial f}{\partial r} e_r+ \frac{1}{r sin\theta}\frac{\partial f}{\partial \phi} e_{\phi}+ \frac{1}{r}\frac{\partial f}{\partial \theta} e_{\theta} p=(r,\phi,\theta) and...

I just did a quiz in a lecture and walked out crying. There was one question (which probably seems very easy to most :/ ) were you had to convert polar equations to cartesian ones. We also had to draw the cartesian graphs (2D). a) rcos(th) b)r=2asin(th) c)r^2sin2(th)=2k...

Homework Statement Find the limit of lim_{(x,y) \rightarrow (0,0)} xy(\frac{x^{2}-y^{2}}{x^{2}+y^{2}}) Homework Equations The Attempt at a Solution We were supposed to switch to polar coordinates to solve this problem. Thus we get, lim_{(r) \rightarrow (0)} rcos\theta rsin\theta...

Homework Statement I've got this problem on polar coordinates which says: A particle moves along a plane trajectory on such a way that its polar coordinates are the next given functions of time: r=0.833t^3+5t \theta=0.3t^2 Determine the module of the speed and acceleration vectors for this...

I was perusing an astronomy homework site and came across a question in which they are asked to plot the positions of the 3 inner planets on polar graph paper. They are then asked questions about visibility and time of day in Earth's sky. The table: [FONT="Courier New"] Location Venus Earth...

Homework Statement I've got some trouble and doubts with polar coordinates. I have this exercise, with a rocket going upwards, with a given acceleration. So I need to find the polar equation for the given situation for the position, the velocity and the acceleration. How should I proceed? I...

Homework Statement When you substitute polar coordinates into a multivariable limit, do you treat theda as a constant when evaluating? (I know how to use polar coordinates to evaluate a limit but haven't learned what they are yet) Homework Equations The Attempt at a Solution

Homework Statement Homework Equations The Attempt at a Solution Please tell me if I am wrong. I suspect about the ranges. Are my range corrrect?

This particular problem is just confusing me in the setup. I need to find the area that is inside both: r=sqrt(3)cos(theta) and r=sin(theta) It makes a petal type shape. I was beating my head around for a while, but I reasoned that since the equation used to find the area cuts out in a straight...

Homework Statement In Cartesian coordinates the magnitude of the velocity vector squared is |v|^2=V*V= Vx^2 +Vy^2 =(dx/dt)^2+(dy/dt)^2 Show that in polar coordinated |v|^2= Vr^2 +V@ ^2 Homework Equations The Attempt at a Solution Not really sure what the question is asking me to...

Homework Statement H(F) = 5/(1+j2piF/10) Rewrite in polar form, that is, in terms of magnitude and phase. Homework Equations The Attempt at a Solution phase is the 2piF/10 but I'm not sure how I account for it being on the bottom of the fraction

Well this problem started off simply enough. I was given this function: r=2cos(3\theta) And I had to find the area bound by it. I sketched it out from zero to 2pi and got this...

I know that a complex number can be written in form of a+bi and r(cos(theta) + isin(theta)) but I don't understand the the representation of it as r*e^(i * theta) also

Homework Statement Well, I've made a double limit using the polar forms. The thing is the limit is wrong, I've made a plot, and then I saw that the limit doesn't exist, and what I want to know is what I'm reasoning wrong, and some tips to get a deeper comprehension on this limits, and on what I...

I'm having issues getting converting Polar functions to Cartesian functions. Take for example: rcos(\theta)=1 I just figured that since it was going to always equal the same thing, and because x=rcos(\theta) that the Cartesian equation was x=1, and I was right. However logic fails...

It seems to me that integrating a polar equation should give you the arc length of the curve, rather than the area under it. This is my reasoning: A polar equation is in the form of: (1) r = f(\theta) The arc length of a segment of a circle where the radius is constant is given...