Polar coordinates Definition and 569 Threads

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".

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...

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 "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...

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...

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...

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...

[FONT=arial]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. [FONT=arial]Please help

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 "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...

Homework Statement A particle moves with constant speed v around a circle of radius b. Find the velocity vector in polar coordinates using an origin lying on the circle. https://www.desmos.com/calculator/maj7t9ple1 Imagine the r starts at (0,0). Homework Equations \frac{d\vec{r}}{dt} =...

Homework Statement Show that: I = \int\int_{T}\frac{1}{(1 + x^{2})(1 + y^{2})}dxdy = \int^{1}_{0}\frac{arctan(x)}{(1 + x^{2})}dx = \frac{\pi^{2}}{32} where T is the triangle with successive vertices (0,0), (1,0), (1,1). *By transforming to polar coordinates (r,θ) show that:* I =...

Homework Statement The quality of the image is bad so here's the statement: For an interval of motion the drum of radius b turns clockwise at a constant rate ω in radians per second and causes the carriage P to move to the right as the unwound length of the connecting cable is...

Homework Statement I know I have the set up done correctly I am wondering where I went wrong because I know I cannot get zero, and I am a little worried I did my integration wrong. please help. http://i1341.photobucket.com/albums/o745/nebula-314/IMAG0107_zps3cde35a8.jpg

I've always been curious why points in polar coordinates are defined as (r,θ) when all equations (including parametric equations formed from them) are defined as r=f(θ). Considering that point in cartesian coordinates are defined as (x,y) where y=f(x). Also a,b=(r,θ) ∫1/2[f(θ)]2 further...

Homework Statement A tourist takes a tour through a city in stages. Each stage consists of 3 segments of length 100 feet, separated by right turns of 60°. Between the last segment of one stage and the first segment of the next stage, the tourist makes a left turn of 60°. At what distance...

Homework Statement Find the area in the polar curve r = sin2θ between 0 and \frac{\pi}{2}. The way to do this is to say the area of a tiny bit of this polar curve, dA = \frac{1}{2}r^{2}dθ so the integral is just \frac{1}{2}\int^{\frac{\pi}{2}}_{0}(sin2θ)^{2}dθ if we did say a function...

Homework Statement Change of coordinates from rectangular (x,y) to polar (r,θ). Not sure what's wrong with my working.. Homework Equations The Attempt at a Solution

Spherical, Cylindrical or Polar Coordinates Homework Statement I have attached an image of the problem. I know that the solution is number 1 but I'm having some difficulty understanding why. In solution one is it using cylindrical coordinates> My first response to this question had been to...

Homework Statement Take the double integration of http://webwork.usi.edu/webwork2_files/tmp/equations/08/1294e87299342c0ccfe2f8a97055da1.png when f(x)=sqrt(4x-x^2) Homework Equations x=rcos(theta) y=rsin(theta) The Attempt at a Solution I know I plug in the r*cos(theta) and...

Homework Statement Consider the complex function f (z) = (1 + i)^z with z ε ℂ. 1. Express f in polar coordinates. Homework Equations The main derived equations are in the following section, there is no 'special rule' that I (to my knowledge) need to apply here. The Attempt at a...

Hello all, I've been going through Bernard Schutz's A First Course In General Relativity, On Chapter 5 questions atm. Should the Christoffel Symbols for a coordinate system (say polar) be the same for vectors and one-forms in that coordinate system? I would have thought yes, but If you...

The question is in the paint document I wanted to know why they integrated from 0 to pi and not from 0 to 2pi

Homework Statement Using polar coordinates, show that lim (x,y)->(0,0) [sin(x^2+y^2)]/[x^2+y^2] = 1 Homework Equations r^2=x^2+y^2 The Attempt at a Solution I was able to get the limit into polar coordinates: lim r->0^+ [sin(r^2)]/r^2 but I'm not sure how to take this limit. I tried...

Hi everyone. I am a little desperated cause my exam is on monday and still much stuff to do. I don't get when I am supposed to use/consider radial and tranversal forces. Most excercises say "it rotates on the horizontal or vertical" I guess this is the info that tells me if there is...

I have never solved an equation in polar form. I am not sure with how to start. Solve Laplace's equation on a circular disk of radius a subject to the piecewise boundary condition $$ u(a,\theta) = \begin{cases} 1, & \frac{\pi}{2} - \epsilon < \theta < \frac{\pi}{2} + \epsilon\\ 0, &...

Homework Statement Hi, I'm trying to find the area of a circle in polar coordinates.I'm doing it this way because I have to put this into an excel sheet to have a matrix of areas of multiple circles. Here is an example of the problem. a= radius of small circle (gamma, r0) = polar coordinate...

Hi, I'm trying to find the area of a segment of a circle that is not at the origin. It will look similar to this picture below but I need to find the area enclosed by a circle. Using the polar equation of a circle provided by wikipedia: and integrating to find the area of a...

Homework Statement from the cartesian definition of angular momentum, derive the operator for the z component in polar coordinates L_z = -ih[x(d/dy) - y(d/dx)] to L_z = -ih(d/dθ) Homework Equations x = rcosθ y = rsinθ r^2 = x^2 + y^2 r = (x^2 + y^2)^1/2 The Attempt at...

Hi, I have a pretty simple question but I'm not certain I know how to phrase it properly. I will try. When we are integrating using cartesian coordinates to find the area under a curve, area under the x-axis is negative and area above the x-axis is positive. This makes sense when I...

When plotting graphs in polar coordinates, how does one know when to make the graph sharp (at θ=0) (as in for the graph for r=1-cosθ) as opposed to a dimple (r=3/2 + cos θ) ?

Homework Statement Integrate y/(x^2+y^2) for x^2+y^2<1 and y> 1/2 ; use change of variables to polar coordinates Homework Equations THe above The Attempt at a Solution the variables transform as y=rsinz x=rcosz, where z is an angle between pi/6 and 5*pi/6 = which is the...

Homework Statement I'm not grasping how to convert a surface with known rectangular graph to a parametric surface (using some polar techniques, I assume). I would appreciate it if someone could clarify the conversion process. One of the examples is as follows: A sphere...

Hey all, I've never taken a formal class on tensor analysis, but I've been trying to learn a few things about it. I was looking at the metric tensor in curvilinear coordinates. This Wikipedia article claims that you can formulate a dot product in curvilinear coordinates through the following...

Hi, I am learning about Polar Coordinates and how they can be written in several equivalent ways. I understand how you can add 360 to angles and use negative angles to represent the same point. However, I have a very hard time understanding how you can write the same point but with a...

Homework Statement Sketch the curve r = 1 + 2cosθ in polar coordinates. Homework Equations None that I can think of, it's graphing. The Attempt at a Solution What I was trying to was use the method of finding cartesian coordinates and plugging different values of θ into the equation to...

Homework Statement Plot the Following points(given in polar coordinates). Find all the polar coordinates of each point. a. (2, pi/2) b. (2,0) c. (-2, pi/2) d. (-2,0) Homework Equations none The Attempt at a Solution I have plotted it on a graph but could someone explain to me...

Hi, I need some help understanding the solution to a problem. Equations: x = r.cos(θ) y = r.sin(θ) r = x2 + y2 theta = arctan(y/x)Question: Determine the Jacobian Matrix for (x,y)T and for (r, θ)T SOLUTION: I understand and can compute by myself the Jacobian for (x,y)T, but the solution to...

I'm trying my very best to understand it, but really, I just couldn't get it. I read four books now, and some 6 pdf files and they don't give me a clear cut answer :( Alright, so this integral; ∫e-x2dx from -∞ to ∞, when converted to polar integral, limits become from 0 to 2∏ for the outer...

Homework Statement Do you see how y gets converted to csc? I don't get that. I would y would be converted to sin in polar coordinates.

Homework Statement a elliptic paraboloid is x^2/a^2+y^2/b^2<=(h-z)/h, 0<=z<=h. Its apex occurs at the point (0,0,h). Suppose a>=b. Calculate the volume of that part of the paraboloid that lies above the disc x^2+y^2<=b^2.:confused: 2. The attempt at a solution We normally do the...

Homework Statement Show that ##\iint_{S}(x^2 + y^2)d\sigma = \frac{9\pi}{4}## where ##S = \{(x,y,z): x > 0, y > 0, 3 > z > 0, z^2 = 3(x^2 + y^2)\}## Homework Equations ##\iint_{S}f(x,y,z)d\sigma = \iint_{R}f(r(x,y))\sqrt{[r_x(x,y)]^2 + [r_y(x,y)]^2 + 1}## where ##r : R → ℝ^3, R \in ℝ^2##...

Homework Statement It is given a set defined as: 0≤x≤1, 0≤y≤1-x. With x,y in ℝ. f(x,y)=1 (plane parallel to Oxy plane) They ask you to express the integral ∫∫Setf(x,y)dxdy in polar coordinates and calculate it. Homework Equations x=rcosθ y=rsenθ r=√x2+y2 The Attempt at a...

Homework Statement find the over lapping area of the following equations r=3sin(x) r=1+sin(x)Homework Equations area =1/2 ∫ f(x)^2 dxThe Attempt at a Solution first off I started by finding the intersecting angle by: 3sin(x)=1+sin(x) 2sin(x)=1 sin(x)=1/2 x=pi/6 and the peak is at pi/2 so I...

I am asked to consider the following graph: r2=a+sin(θ), where a=2 I have a picture of this plot, which I have attached, We are asked to find the area of the upper 'cresent' of the curve, contained at the top How would I go about calculating that? I've found that if I plot...

Homework Statement Use polar coordinates to evaluate: ∫sqrt(2)0 ∫sqrt(4-y2)y 1/(1+x2+y2) dxdy Homework Equations The Attempt at a Solution I graphed it and I see r is the part of the elipse sqrt(4-y2) and goes from 0 to ∏/4. I'm not sure how to make the bounds for r or how to...