Polar Definition and 1000 Threads

Hey, everyone. I'm new to the forums and am hoping that someone can help me with a tricky problem from my multivariable calculus class. We're covering double integrals in polar coordinate systems, and there's a problem from my problem set for homework that I can't seem to get the grasp of. The...

Homework Statement Ok so for circular motion we have v = w x r where w and r are vectors.. my question s very simple..what is the vector w? Homework Equations The Attempt at a Solution

Goldstein(3rd) 1.15 Generalized potential, U as follows. U( \stackrel{\rightarrow}{r} ,\stackrel{\rightarrow}{v})=V(r)+\sigma\cdot L L is angular momentum and \sigma is a fixed vector. (b) show thate the component of the forces in the two coordinate systems(cartesin, spherical...

Homework Statement I have to find all of the points of intersection of the curves... r2 = sin(2θ) r2 = cos(2θ) The Attempt at a Solution sin(2θ) = cos(2θ) 2sinθcosθ = cos2θ - sin2θ 2sinθcosθ - cos2θ = -sin2θ cosθ(2sinθ - cosθ) = -sin2θ This is where I'm having a problem, I'm...

Homework Statement Convert to polar coordinates to evaluate \int^{2}_{0}\int^{\sqrt(2x-x^2)}_{0}{\sqrt(x^2+y^2)}dydxThe Attempt at a Solution Really I'm just not sure how to convert the limits of integration. I know \sqrt(2x-x^2) is a half-circle with radius 1, but I'm not really sure where...

Homework Statement Transform the equilibrium equations from cartesian to polar coordinates using x = rcos(theta) and y = rsin(theta): \frac{\partial\sigma_{xx}}{\partial{x}} + \frac{\partial\sigma_{xy}}{\partial{y}} = 0 \frac{\partial\sigma_{yx}}{\partial{x}} +...

Homework Statement I have to find the area of the region that lies inside the curves: r = sin(θ) r = sin(2θ) The Attempt at a Solution I'm assuming the first step would be to find the points of intersection so I know WHERE to integrate from/to, so I set the equations equal to each...

I'm studying for a maths test. I know that the second derivative of the position R(t) of a particle moving in the plane, in polar coordinates, is (r''-r(\vartheta')2)er + (r\vartheta''+2r'\vartheta')eo. o = \vartheta How to differentiate this to find R'''(t), in polar coordinates and...

Homework Statement Show that the equation below connects the point (r_{0}, \theta_{0}) to the point (r_{1}, \theta_{1}), \theta_{0}\neq\theta_{1}, along a curve that everywhere forms the same angle with the rays \theta=constant. And here's the equation. I can't get the Latex to work... no...

Homework Statement Use polar coordinates to find the volume of the solid enclosed by the hyperboloid -x^2-y^2+z^2=1 and the plane z=2. The Attempt at a Solution Solving for z of the equation of the hyperboloid I find z = Sqrt(1 + x^2 + y^2). Letting z = 2 to determine the curve of...

Hi, so I scanned an image of the problem statement and my attempt at the solution. I don't know if I am headed in the right direction and need some guidance. This is my first post ever and I hope I am doing this properly. Thank you for any help you guys can provide.

Homework Statement Find the polar form of 2i − 1 Finding polar form is easy r(cosx + isinx) call the real part a and imaginary part b r = sqrt(a+b) theta = arctan (-2) = - 63.43 This is the wrong angle for theta as it's 116.57 (which is 180 - 64.43), and I guess this if...

Homework Statement Evaluate \int\intT (x^2+y^2) dA, where T is the triangle with the vertices (0,0)(1,0)(1,1) Homework Equations The Attempt at a Solution \int d\theta \int r^3 dr Thats how far I got, not really sure about boundries on r. First integrals boundrie should be 0 to pi/4. Is...

Homework Statement Solve the Laplace equation: delta u = d2u/dx2+d2u/dy2 inside the half disk 0<r<R, 0<phi<pi Temperature on the bottom side of the disk is zero, u(x,y=0)=0. Temperature on the upper side of the disk is u(r=R, theta) = u0(phi), 0<phi<pi Homework Equations I'm...

Homework Statement evaluate i^1/4 Homework Equations - The Attempt at a Solution don't know how to find the angle on argd

Hello, its been a pleasure finding you:smile: I have an asignment due to the end of this week and due to some problems, i hadn't found time to get to it so far. I have to calculate the exact solution of the Laplace equation in polar coordinates, in a hollow disk in the domain Ω where...

How are the Arctic natives of America similar to those of Eurasia?

Homework Statement Convert t = pi/6 into polar form. Homework Equations x = r*cos(t) y = r*sin(t) The Attempt at a Solution t = pi/6 cos(t) = cos(pi/6) cos(t) = sqrt(3)/2 x/r = sqrt(3)/2 sqrt(3)r = 2x sqrt(3)sqrt(x^2 + y^2) = 2x sqrt(3x^2 + 3y^2) = 2x 3x^2 + 3y^2 = 4x^2...

Hello, I posted a similar question long time ago, but after working on it I am still unable to arrive at a solution. Let's have a group of linear transformations (rotations in the xy-plane): R_\theta=\{ (\begin{array}{ccc} cos\theta & -sin\theta \\ sin\theta & cos\theta \end{array}) \\ ...

Homework Statement A particle of mass m is constrained to slide on the inside of a vertical smooth semi- circular ring of radius r. The position of the particle is described by a polar coordinate system whose origin is at the centre of the circle with axes along the orthogonal unit vectors...

Homework Statement Find the cartesian equation for the curve r=csctheta The Attempt at a Solution I understand how to get the answer, by changing it to r=1/sin, and then rsin=1, and then since y=rsin, then y=1. What I'm not understanding is the relationship between y=1 an r=csc. I...

Hey guys, I have attached the question with the diagram. So far i have found my magnitude of velocity = 90mm/s. im just really stuck now, i can't find my angle to find my components Vr and V(theta) I also know that you can solve this problem by finding a relationship between theta and "r"...

Homework Statement What is the polar form of the complex number 3-4i? Homework Equations z=r*cos(theta)+i*r*sin(theta) The Attempt at a Solution 5(cos(arctan(-4/3))-i*sin(arctan(-4/3))) This is what I thought the correct answer would be, but it was a multiple choice quiz and...

Hi I have a homework set due this week, 14 problems, I have done 11 of them, but these 3 are giving me trouble, help would be great :) Homework Statement 1.A cylindrical drill with radius 4 is used to bore a hole through the center of a sphere of radius 8. Find the volume of the ring shaped...

Homework Statement The question is: Factor and Plot the polar equation r^2-r+(1/4)sin^2 4 theta Homework Equations N/A The Attempt at a Solution I have no idea how to do this.

Hi All, This is my first post. I am an Electronics Engineer and came by this great forum while searching something for my presently running project. Could anyone please help me with the following: I have two points A(magnitude1,phase1[deg]) and B(magnitude2,phase2[deg]) on the input side...

Homework Statement a) r=a(2+ cos(\theta)) Find the area of the region enclosed by the curve giving answers in terms of \pi and a b) Show that the area enclosed by the loop r=2(1-sin(\theta))\sqrt{cos(\theta)} is \frac{16}{3} and show that the initial line divides the area...

Homework Statement Two globular clusters A and B have cylindrical polar coordinates relative to the centre of the galaxy (r, z, Ø) given by A = (5,2,15°) and B= (4.6,65°), where the r and z coordinates are in kiloparsecs. Homework Equations Find a and b the position vectors of each...

Homework Statement Find the area between the two curves: r=2sin(\theta), r=2(1-sin(\theta)) Homework Equations A=\frac{1}{2} \int_{\beta}^{\alpha} r^2 d\theta The Attempt at a Solution I've got the points of intersection at (1,\frac{1}{6}\pi) and...

Homework Statement By transforming to polar coordinates, evaluate the following: \int^{a}_{-a}\int^{\sqrt{}{{a^2}-{x^2}}}_{-\sqrt{{a^2}-{x^2}}}dydx Homework Equations The Attempt at a Solution I can get the right answer to this but only after guessing that the inner limits...

Homework Statement (1+i)i = reiθ Find the real values of r and θ. The Attempt at a Solution Well, after doing a similar(ish) question I decided taking logs would be a good start: i loge(1+i) = loger + iθ From here, I have no idea where to go. Using a power of i is killing me...

Homework Statement a) Find the area enclosed by the curve r=2+3cos(\theta). b) Find the area enclosed by the curve (x^2+y^2)^3=y^4 (after converting to polar form) Homework Equations The general equation for the area of a sector of curve: A=\frac{1}{2} \int_{\beta}^{\alpha} r^2...

Homework Statement Which would be the stronger nucleophile in a polar aprotic solvent? a) H2O or H2S b) (CH3)3P or (CH3)3NHomework Equations The Attempt at a Solution I'm really confused because in my book, it says that in protic solvents, the larger atoms (I-) are stronger nucleophiles than...

Is it correct that the angle of intersection of two curves is the same in x,y coordinates as in r,theta coordinates? If so, why is this?

Homework Statement Using Green's Theorem, (Integral over C) -y^2 dx + x^2 dy=____________ with C: x=cos t y=sin t (t from 0-->2pi) Homework Equations (Integral over C) Pdx + Qdy=(Double integral over D) ((partial of Q w.r.t. x)-(partial of P w.r.t. y))dxdyThe Attempt at a Solution I'm...

Homework Statement Establish an equation in polar coordinates for the curve x^2+y^2=4y-2x Homework Equations n/a The Attempt at a Solution I know that x^2+y^2=r^2 so I used substitution, and now have r^2=4y-2x. Now this next part, I'm really not sure if I'm allowed to do this... i...

Hi, 1st year chem guy here...I'm missing this idea. Is it all based upon Electronegativity? I can see why HBr or HCl and other 2 atom compounds would be polar. 2 atoms with different charges or even sizes creating an un-even pull. I'm guessing H2O is polar as the 4 remaining electrons on...

what'd I do wrong? I was told I didn't include the bound y<=x but that still hasn't helped me figure out where I miss stepped thanks -Ben

Double Integrals: cartesian --> polar and solve here is everything: #19: I am stuck...This is to be solved using cylindrical polar coordinates and a double integral. I understand simpler ones such as find the volume of the solid under the cone z= sqrt(x^2 + Y^2) and above the disk (x^2 + y^2...

Homework Statement Particle is moving with velocity v= ui along the line y=2. What is its v in polar coordinates Homework Equations The Attempt at a Solution I think I'm being really stupid here but not entirely sure where to start. If you integrate to find position you have it as...

Homework Statement Find the area cut from the surface z = 2xy by the cylinder x^2 + y^2 = 6. [Hint: Set up the integral using rectangular coodinates, then switch to polar coordinates.] Homework Equations A = \iint \sqrt{{z_x}^2+{z_y}^2+1}dxdy = \iint...

Hi guys Can anyone explain what is physical significance polar moment of inertia. Well i know it's formula e.g in case of shafts but not it's physical meaning.

Some chem students need help with homework problems similar to these later this week. and I want to make sure I've got the concepts down before I try to explain anything. This is for introductory chemistry. 1. Can a molecule have only nonpolar bonds and have a dipole? My first thought was...

Homework Statement Let the curve C be paramatized into polar coordinates given by: \[r\left( t \right)=\left( r\left( t \right)\cos \theta \left( t \right),\,\,\,\,\,r\left( t \right)\sin \theta \left( t \right) \right),\,\,\,\,\,a\le t\le b\] where r and theta is continuous derivatives...

Use polar coordinates to find the volume of the given solid inside the sphere x^2 +y^2 + z^2 = 16 and outside the cylinder x^2 +y^2 = 4 I know how to set up the the integral to find the volume inside the sphere but I am not quite sure how to also find the outside of the cylinder. Can someone...

Homework Statement Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. int(-1to1)int((sqrt(1-y^2))to(sqrt(1-y))[x^2+y^2]dxdy Homework Equations x=rcostheta y=rsintheta The Attempt at a Solution...

Homework Statement 1. put in polar form x2+y2-3x+4y=0 my work: x2+y2=3x-4y r2=3rcos\theta-4rsin\theta r=3cos\theta-4sin\theta 2. put in cartesian form r2=tan\theta r2=y/x r=sqrt(y/x) 3. find slope at \theta=\pi/2 then find points where tangent line is horizontal...

Homework Statement Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles x^2 + y^2 = 4 and x^2 - 2x + y^2 = 0 Homework Equations The Attempt at a Solution for my integral i got 0<= theta <=pi/2 for the theta...

Homework Statement r1= 1+sin(theta) r2= 5sin(theta) Homework Equations see above? The Attempt at a Solution totally stumped. usually i would set the two curves equal to each other, but i have no idea how to do that. using my ti-89's solve function just gives me a weird answer...

Homework Statement Convert to polar integral and integrate. \int_{D}\int xy dA where D is the disk with the center origin and radius 3. I am not sure about the limits. I know that x = rcos(\theta), y = rsin(\theta), dA = rdr*d\theta