Polar Definition and 1000 Threads

Homework Statement Derive the equations for the velocity and acceleration vectors of a particle in polar coordinates. 2. The attempt at a solution r = xi + yj where x = rCos\Theta, y = rSin\Theta r = r(Cos\Thetai + Sin\Thetaj) v = \frac{d}{dt}r v = \frac{d}{dt}[r(Cos\Thetai +...

Homework Statement Evaluate the integral integral from 0 to 1 of (integral from y to sqrt(2-y^2) of (3(x-y))dxdy) by converting to polar coordinates. Homework Equations x = rcos(theta) y = rsin(theta) The Attempt at a Solution By drawing a picture of the bounds, I...

Hey, I have the following integral: I = \int_0^\infty dx_1\ldots \int_0^\infty dx_{3N} \int_0^\infty dy_1\ldots \int_0^\infty dy_{3N}\Theta\left(1-\sum_{j=1}^{3N}\left(|x_j|^2+|y_j|^2\right)\right) Now I want to change to polar coordinates by the following substitution...

I really, really need to know the formula that adds (or subtracts) two complex numbers in polar form, and NOT in rectangular form. I know there is such formula (I saw it in some book), and it's composed of cosines and sines. Please, please don't tell me to convert back to rectangular form...

Find the volume under the cone z = sqrt ( x2+y2 ) and on the disk x2+y2 < 4. Use polar coordinates. Graphing x2+y2 < 4, I get a circle centered at 0,0 with radius of 2 So theta goes from 0 to 2pi Also, since x2+y2 < 4 This means that r^2 < 4 so -2 < r < 2...

The angular momentum of the Bohr atom is ⃗L = ⃗r× ⃗p Let the Oz axis of the unit vector ⃗uz be determined by the relation L = L⃗uz, in which L stands for the magnitude of the angular momentum vector ⃗L . (Basically L is in Positive z axis) We specify the position of the electron within its...

N-F C-F H-F O-F would it be H-F since the difference between the their electronegativities is the greatest?

Homework Statement \displaystyle\int\int\sqrt{4-x^2-y^2} dA R{(x,y)|x^2+y^2\leq4 .. 0\leq x} The Attempt at a Solution So far i have: \displaystyle\int^{\pi}_{0}\int^{r}_{0}\sqrt{4-r^2} rdrd\theta Solving i get...

Hi I want check my answer 4 - write answer in both rectangular from and polar Q in degre a ) (1 + i ) ( 2+ 2i ) b ) -2 + 2i

Homework Statement This is a subtask. I was given a function, and then asked to convert it to polar coordinates. So I did, and I also determined the limit. However they ask me to do an epsilon-delta proof. The function is: f(x,y)=\frac{x^6 + y^8 + x^4y^5}{x^6 + y^8}, which converted to polar...

Hi I want check my answer if correct or not write in rectangular form 1) Z2 = 3e^(-60)i 2) z3 = 7.19e^-2.13i 3) z1 = root2 e^(-pi/2)i 4)z2 = 3e^120i 5 ) z3 = 6.49e^-2.08i ------ my answer : 1) = 3{cos (-60 ) + i sin ( -60) }...

write in polar form ...elc -3 - 5i my answer : x = -3 y = - 5 r = root (-3)^2 + (-5)^2 = 5.83 tan Q = 5/3 = -1.12 tan-1 -1.12 = -0.84 Q = -0.84 Q = -pi + -0.84 = -3.981 Polar form = 5.83e^(-3.981)i

Hi I face some problem when i try to find tan in like this questions for example : write in polar z1 = 1 - i the answer is -5π/4 but my answer is tan Q = y/x = -1/1 = -1 how I get -5π/4 -------------- ex : 2 z = -root3 + i my answer...

Homework Statement integrate f(x,y) = sqrt(x^2+y^2) over triangle with vertices (0,0) (0,sqrt2) (sqrt 2, sqrt 2) Homework Equations x= rcosO, y = rsinO x^2+y^2=r^2 The Attempt at a Solution im supposed to use a double integral converted to polar coordinates, so i used...

Hello, If we consider a Euclidean plane \mathbb{R}^2 with the ordinary inner product, and we "distort" it through a cartesian->polar transformation, how should I compute the shortest arc between two points (r,\theta) and (r',\theta') ?

Homework Statement Ok so I solved the problem, I think. I would just like to check my work. So the problem is: Use polar coordinates to find the volume of the given solid bounded by the paraboloids z = 3x^2 + 3y^2 and z = 4 - x^2 - y^2. Homework Equations r^2 = x^2 + y^2 x = r cos...

Homework Statement Find the total length of the cardioid r=a(1-cos theta) Homework Equations ds2=r2dtheta2+dr2 ds= integral from beta to alpha sqrt[r2 + (dr/d theta)2]dtheta The Attempt at a Solution dr=a(sin theta)d theta ds2=a2(1-cos theta)2d theta2 + a2sin2theta (d...

Homework Statement Consider the graph (see attachment) of r = 1 +2cos\Theta in polar coordinates. SET UP integrals to find 1. the area inside the large loop minus the area of the small loop. 2. the arc length of the small loop 3. the surface area of the surface formed by...

1. Use polar coordinates to find the volume of the given solid. 2. Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.

polar set... Excuse me for my poor Latex ability. I type my question in WORD. The follow is the URL of the problem... http://img714.imageshack.us/img714/8185/matht.jpg

Homework Statement x=r*cos(theta) y=r*sin(theta) Ur=Ux*cos(theta)+Uy*sin(theta) Utheta=-Ux*r*sin(theta)+Uy*r*cos(theta) Vr=Vx*cos(theta)+Vy*sin(theta) Vtheta=Vy*r*sin(theta)+Vx*r*cos(theta) cauchy rieman equations, Ux=Vy Uy=-Vx and for polar Ur=(Vtheta)1/r Vr=(Utheta)(-1/r) show that...

"interactions between polar materials and electric field" sorry typing error.polar materials are those who have a permanent dipole ( like water molecules ) but these dipoles doesn't appear on the macroscopic scale due to their random orientation , so what if this polar medium is subjected to...

Using polar coordinates to find the volume of a bounded solid[Solved] I found the equation of the boundary circle by setting z to 4 in the paraboloid. Then I did some work to get polar coords: x^2+y^2 = 1 x^2+y^2 = r^2 1-x^2-y^2 = 1-r^2 Then I set up my integral as such...

Hi I pretty much can't get past the first chapter in my physics book until I master the vector representation of polar coordinates. Every explanation I've read thus far has confused me, I keep thinking in Cartesian terms so I think it'd be great to convert a vector equation from cartesian to...

1. Find the area of the region described: a) inside one loop of the lemniscate r^2=4cos(2theta) b) inside the six-petaled rose r^2=2sin(3theta) [b]2. A=integral [1/2 r^2 dtheta] Are there any easy ways to determine the integration bounds? (without graphing) Our textbook doesn't give any...

Hii guys.I have this problem.Can anybody help me on this.tq Homework Statement A satellite is in a circular polar orbit at a height of 870 km, the orbital period being approximately 102 min. The satellite orbit passes directly over a beacon at sea level. Assuming an average value of...

Hi, I've been having some issues in solving this problem. Homework Statement Find the arc length of r=2/(1-cosθ) from π/2 to πHomework Equations L =(integrate) sqrt(r2+(dr/dθ)2)dθ The Attempt at a Solution I found (dr/dθ) = (-2sinθ)/(1-cosθ)2 so (dr/dθ)2 = (4sin2θ)/(1-cosθ)4 Then r2 =...

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...