Polar Definition and 1000 Threads

In polar coordinates we have \vec{r} = r \hat{r} \Rightarrow \vec{v} = \frac{d}{dt}({r \hat{r}}) = \dot{r}\hat{r} + r \frac{d \hat{r}}{dt} . In the book Introduction to Mechanics, K & K says the right term is the component of velocity directed radially outward. (Surely a typo, as the left...

How to translate r = 2 /(2 - cos(theta)) to cartesian coordinates: so far: r = 2 /(2 - cos(theta)) r = 2 /(2 - cos(theta)) |* (2 - cos(theta)) both sides r (2 - cos(theta))= 2 2*r - rcos(theta) = 2 | know x = rcos(theta) 2*r - x...

I know that \oint_{C}\mathrm{d}\vec{l} = 0, for any closed curve C. But when i try to calculate the integral around the unit circle in polar coordinates, I get a result different from zero. Here is my approach : \oint_{C}\mathrm{d}\vec{l} = \int_{0}^{2\pi}\hat{\phi}\mathrm{d}\phi =...

Here is the question: Here is a link to the question: R= 4 / (1 - 3 sin theta)? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Trying to help someone out with their assignments on basic polar graphs. This first question is very easy to determine the poles from as the limacon has an inner loop. But when you have a limacon WITHOUT (below) an inner loop, how does the "max from pole" and "min from pole" figure? It's been...

Hello =] I'm having trouble with this question, can somebody please help me with it! I'll thanks/like your comment if help me =) ![Question][1] I know that for a ellipse the parametric is x=a sin t , b= b cos t t:0 to 2pi (?) for part a) I drew up the graph but not sure if it's...

Homework Statement Find a polar equation with the graph as xy=16 Homework Equations r = ed/(1+- cos\theta)? I'm not really sure at all. The Attempt at a Solution I also tried using x = rcos\theta and y = r sin\theta but I can't get anything. I know it's a hyperbola.

Can anyone point me to a derivation of the navier stokes equations in polar? I don't see where the single derivative in theta terms are coming from in the first 2 components.

When it comes to converting Cartesian to polar coordinates, I sometimes still get mixed up on how to define the angle theta (if its -π <= theta <= π , or 0 <= theta <= 2π for example) depending on the position of the surface etc. Can anyone shed light on the definitive way on how to set this...

Homework Statement A 90Ω resistor, a 32 mH inductor, and a 5μF capacitor are connected in series across the terminals of a sinusoidal voltage source Vs = 750cos(5000t + 30)V. Calculate the phasor current. Homework Equations phasor current i = V/Z V in polar form = (Magnitude)(cos a + j sin...

Homework Statement Homework Equations The Attempt at a Solution my only problem curently is in finding the angle θ. I do get the equation x^2 + y^2 =1 however am confused whether this would be a semi-circle on the positive axis or a full circle. because my teacher has notes that...

Homework Statement Find polar coordinates. Homework Equations Cartesian: (-3,4) The Attempt at a Solution r = sqrt(9+16) = 5 sinθ = 4/5 cosθ = -3/5 θ = ∏ - arctan(4/3) Answer: (5, ∏ - arctan(4/3)) I do not understand why we have subtracted the value arctan(4/3) from pi?

Is there a way to find all points of intersection in a polar co ordinate graph without the need to draw the graph. i/e USing algebra? If so, how?

I understand how to derive the divergence in polar. Ok, so I have the formula. But what I am confused about is this: say u=(0,0,w(r)), so as you can see the third component of this vector u is in fact a function of r. If I plug this into the polar divergence formula, I get zero, fine. But...

Homework Statement Curve C is given in Polar Coordinates by the equation r=2+3sinθ. Consider the usual Cartesian plane and take O as the pole and the positive x-axis as the polar axis. Find points on the curve C where the tangent lines are horizontal or vertical and sketch the curve C...

Homework Statement Is this molecule polar or non polar? What is its dipolar moment? Homework Equations The Attempt at a Solution The molecule has triple symmetry so its dipolar moment is 0. But I think it is polar because the oxygens atract the eletrons much more strongly...

Homework Statement Solve the BVP: r^{2}u_{rr} + ru_{r} + u_{ψψ} = 0 0 ≤ r ≤ 1, 0 < ψ < 2π u(1,ψ) = 0.5(π - ψ) Homework Equations The Attempt at a Solution I've derived the general solution of u(r,ψ) = C + r^{n}Ʃ_{n}a_{n}cos nψ + b_{n}sin nψ, where a,b, C are...

Homework Statement I have a path defined in polar coordiantes defined as r=a*cos2(θ). I also have the velocity along this path as a function of θ. I want to find the time take to move between two given angles on the path.2. The attempt at a solution I know that this problem will involve some...

Homework Statement Here is a picture of the situation http://i48.tinypic.com/vnmi5t.jpg Homework Equations polar coordinate system The Attempt at a Solution ok so first I'm attempting to find velocity as a function of time, first I know V=(dR/dt)er +(R)(d∅/dt)e∅ - this is a...

Hellow MHB, I'm trying to understand how can i pass this integral to polar coordinates. My biggest doubt is about the "radius".

Hello, I am working on a question in a GFD textbook about tea leaves collecting in the center of the cup regardless of the direction that the tea is stirred. I have an idea of why this is the case but to prove it I need to convert the equation for Ekman pumping to polar coordinates. Its given...

Sketch the 2 polar curves r = -6cos(theta), r = 2 - 2cos(theta). a. Find the area of the bounded region that is common to both curves. b. Find the length around the intersection of both curves. I got a, but I don't know what to do for b because in my calculus book it only shows how to find the...

Hi! I've been given the following problem to solve: Consider the azimuthally symmetric wave equation: \frac{∂2u}{∂t2} = \frac{c2}{r}\frac{∂}{∂r}(r\frac{∂u}{∂r}) where u(r,0)=f(r), ut(r,0)=g(r), u(0,t)=1 and u(L,0)=0. Use the separation of variables method to find the solution to this...

Homework Statement 4{cos(13∏/6)+isin(13∏/6)} = 4((√3/2)+(i/2)) = 2√3+2i Homework Equations The Attempt at a Solution This is an example from my textbook. The part which I do not understand is how to convert the cos and sin of radians into those fractions. Any help is greatly appreciated.

There is a circular gate rotating at a constant angular speed of ω. The circular gate has a tunnel across its diameter. The mission is to pass through the gate. (That is, come in one side of the gate, travel the whole diameter, and exit at the other side.) Also, craft is neutrally buoyant...

Homework Statement Find the area inside both the circles r=2sinθ; r=sinθ+cosθ. Express your answer as an integral, do not evaluate.Homework Equations \int_{\alpha}^{\beta}\frac{1}{2}(r_{1}^{2}-r_{2}^{2})d\thetaThe Attempt at a Solution So I set 2sinθ=sinθ+cosθ and solved for theta = ∏/4 and...

Here is the question: Here is a link to the question: Calculus II Polar Coordinates? I have posted a link there to this topic so the OP can find my response.

Homework Statement Find the area inside the larger loop and outside the smaller loop of the limacon r=.5+cosθ Picture here http://www.wolframalpha.com/input/?i=r%3D.5%2Bcostheta Homework Equations Area = .5∫r^2The Attempt at a Solution To get the area of the outer loop, you just get the value...

Hello all i have a question about adding 3 impedances given in polar form, must i convert them to x..y.. first or is there a quicker way on a calculator and if so can anyone give advice i have the equation Zo=√Z(oc)Z(sc) but finding it hard to understand many thanks.

Homework Statement Find the area enclosed by the graph r=2+sin(4θ) Homework Equations Area = .5∫r^2 The Attempt at a Solution Area = .5∫(2+sin(4θ))^2 =.5(4.5θ-1/16sin(8θ)-cos(4θ)) I can do the integration and all, but I am having trouble finding the limits of integration I...

Homework Statement Find the area of the region that lies inside the curve r^2=8cos(2θ) and outside r=2Homework Equations area of polar curves = .5∫R^2(outside)-r^2(inside) dθThe Attempt at a Solution r^2=8cos(2θ) and r=2, so... 4=8cos(2θ) .5=cos(2θ) since .5 is positive, we need the angles in...

Homework Statement "You are now going to show that, in the Gaussian distribution P(x)=Ae^(-Bx^2) the constant A is equal to sqrt(B/Pi). Do this by insisting that the sum over probabilities must equal unity, Integral(P(x)dx)=1. To make this difficult integral easier, frst square it then combine...

A couple on a cabin holiday at Spitsbergen was rather rattled when a 305 kg male polar bear sought to join them inside by pushing through the window. They had already sent of several warning shots (that is usually enough to make a bear understand he isn't welcome), but this particular bear was...

Firstly; is there a difference between the "regular" polar coordinates that use \theta and r to describe a point (the one where the point (\sqrt{2}, \frac{\pi}{4}) equals (1, 1) in rectangular coordinates) and the ones that use the orthonormal basis vectors \hat{e}_r and...

Hi, Is it correctly understood that all charged molecules are polar (if they have a charge at some point, they must also have a unequal distribution of positivity and negativity) but polar molecules can be charged or uncharged ( they have Δelectronegativity)

Homework Statement Find two other pairs of polar coordinates of the given polar coordinate, one with r > 0 and one with r < 0. Then plot the point. (2, 5π/3)Homework Equations I don't there are any. The Attempt at a Solution I'm not completely sure of how to do this actually. I know that...

I've done this problem and I have a feeling it's incorrect. I've never done a problem like this so I am kind of confused on how else to go about doing it. The goal is to change the cartesian integral $$\int_{-a}^{a}\int_{-\sqrt{a^2-x^2}}^{\sqrt{a^2-x^2}}\,dy\,dx$$ into an integral in polar...

Is it possible to construct Nyquist plot from polar plot (ω varies from ∞ to 0) ?

Homework Statement Evaluate the integral using polar coordinates: ∫∫arctan(y/x) dA Where R={ (x,y) | 1≤ x2 + y2 ≤ 4, 0≤y≤x Homework Equations X=rcos(T) Y=rsin(T) r2=x2 +y2 The Attempt at a Solution First thing was drawing a picture of R, which I think looks like a ring 1 unit thick...

I know that when you are integrated over dA in the xy plane, for your polar coordinates, x = rcosθ and y = rsinθ. However what about in the xz and yz plane? I noticed in one of the textbook problems, where the integration is over an area in the xz plane, x = rcosθ and z = rsinθ. How did the...

Homework Statement Find the curvature of the polar function r = 5sin(2θ). Homework Equations All of the usual curvature equations. The Attempt at a Solution I want to turn this into a vector value function, so I can use the normal curvature equations, but that seems worse. I am...

Homework Statement Given \int^{\sqrt{6}}_{0}\int^{x}_{-x}dydx, convert to ploar coordinates and evaluate. Homework Equations We know that x=rcos\theta and y=rsin\theta and r =x^2+y^2 The Attempt at a Solution First, I defined the region of the original integral: R = 0...

I'm reviewing math material for the EIT exam, I'm going over math concepts that should be pretty basic but I feel like there are gaps in my understanding. I understand how we can use rectangular coordinates and complex numbers to find a point on the complex plane. It would follow logically...

Homework Statement Find the polar form for zw by first putting z and w into polar form. z=2√3-2i, w= -1+i Homework Equations Tan-1(-√3/3)= 5∏/6 The Attempt at a Solution r= √[(2√3)2+(-2)2]=4 tanθ= -2/(2√3)=-1/√3=-√3/3=> acording to above... tan-1(-√3/3)= 5∏/6 so, in polar form z should be...

Hello, I've allways wondered how to get to polar coordinates from cartisan coordinates. I took a course in fluid mechanics but we never learned how to get the continuity equation from cartisan to polar. I know you can use physics to derive the polar equation, but I want to do it just by using...

A circle is drawn through the focus of the parabola $2a/r=1+ \cos( \theta)$ to touch it at the point $\theta=\alpha$. Find the eq. of the circle in polar form. Please help

I'm stuck on the second part of this question. Suppose a particle moves in a plane with its trajectory given by the polar equation $r=2b\sin(\theta)$ for some constant $b>0$. (i) Show that this can be written in Cartesian coordinates as $x^2+(y-b)^2=b^2$. This is the equation for a circle of...

Homework Statement In the attachment, I do not understand how we got the second equation in terms of polar coordinates. Homework Equations The Attempt at a Solution I tried doing it by writing z_dot = (...)z and then plugging in r* exp i theta, but to no avail.

Homework Statement How do I write 1-2i in polar form? Homework Equations The Attempt at a Solution I know r=√5, and when using x=rcosθ, I get angle of 63.43 or 296.57. However, when I take the sin inverse of-2/√5 I get -63.43. I am really confused.

Homework Statement "The shortest path between two point on a curved surface, such as the surface of a sphere is called a geodesic. To find a geodesic, one has to first set up an integral that gives the length of a path on the surface in question. This will always be similar to the integral...