Polar Definition and 1000 Threads

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 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

I'm trying to express the polar rose as an implicit function: r(t)=sin t x = sin t * cos t y = sin^2 t Since sin t * cos t = (1/2) * sin 2t and sin^2 t = (1/2) * (1-cos 2t) (2x)^2 + (1-2y)^2 = 1 4x^2 -4y + 4y^2 = 0 When I plot this, Maple plots a circle, where have I gone wrong?

Homework Statement Give the equations for the plane polar unit vectors ^ ^ r and (theta) - - in terms of the Cartesian unit vectors ^ and ^ and hence show that i j - - ^...

I am going to have a test on polar coordinates next week. What are the most important things to remember?

Homework Statement Calculate the work W_{A B} done by the force F using Newton's laws (F=ma, etc), when a particle moves from the point A to the point B along the unit circle. The angle is \theta. No friction. How do you define kinetic energy in polar coordinates?Homework Equations...

Homework Statement I have a motor with a full load output rating of 2.8 kW with an effciency off 70% and at 80% of full load runs with a Power Factor of 0.8 lagging. A second motor has afull load output of 4.2kW with an effciency of 85% and at 80% of full load runs with a PF of 0.75...

Homework Statement I am having difficulty with a question on my Electrical course and the expressing a motor load voltage and current in polar form. The motor is single phase 2.8 KW efficiency 70% and 80% of full load runs with a power factor of 0.8 lagging. Voltage 400v. Express the motor...

Homework Statement ∫ e^(\pix^2) dx, with limits -∞ to ∞ Homework Equations ∫∫ dxdy = ∫∫ rdrdθ The Attempt at a Solution Hi, here's what I've done so far: Introduce a dummy variable y to get ∫∫ e^\pi(x^2 + y^2) dxdy, with limits -∞ to ∞ for both dx and dy...

Homework Statement \int\int of R ( sin( x^2 + y^2) ) dA where the region 4\leq x^2+y^2 \leq 49 Homework Equations not too sure but i know that dy dx = r d(r) d(theta) The Attempt at a Solution i don't understand how to change into polar coordinates in order to integrate. I'm...

Homework Statement Hi guys I have been given a question, write down w* in polar form where w=2< -(pi/3). I can work out the question when it is in cartesian form just not this way, any help woud be great. Homework Equations The Attempt at a Solution

Find the area enclosed by the curve r=(1+Cos\theta),0\leq \theta \leq 2\pi |cos \theta|\leq1 Maximum r =2(1+1)=4 When r=0, 2+2Cos\theta=0 Cos\theta=-1 Key angle=0 \theta=\pi,3/2\pi Area of curve =1/2\intr^2 dtheta

Homework Statement We define the improper integral (over the entire plane R^2) I as a double integral [-inf,inf]x[-inf,inf] of e^-(x^2+y^2)dA as equal to the lim as a-> inf of the double integral under Da of e^-(x^2+y^2)dA where Da is the disk with the radius a and center at the origin...

I'm sure my question is very simple to most of u guys. But I have the following confusion. Let's say we have an AC voltage source in a circuit. In rectangular form it's phasor form is v= -4 - 16 j . I want to write this phasor in polar form. Well, The phasor is in 3rd quadrant of complex...

Homework Statement A satellite is in a circular polar orbit 240 km altitude. When the satellite is over the South Pole the engine is fired to achieve a polar orbit that has apogee directly over the North Pole. After the impulsive burn an observer on the North Pole observes the satellite has...

Homework Statement http://img162.imageshack.us/img162/9831/97118623.jpg Homework Equations The Attempt at a Solution I first drew R, and from the circle equation, I know the radius of the circle is 12.5. Since the region is in the first quadrant, that'll mean that my limits of...

Homework Statement Rewrite by converting to polar coordinates, carefully drawing R. \int^{2}_{0}\int^{\sqrt{2x-x^2}}_{0}\sqrt{x^2+y^2}dydxHomework Equations The Attempt at a Solution I believe I have the inside part of it right. What I did was replace the x^2 and y^2 in \sqrt{x^2+y^2} with...

Evaluate the integral by changing to polar coordinates \int\int arctan(y/x) Given that 0 \leq x \leq 1 and 0 \leq y \leq x Now I've changed the integral to \int\int \theta r dr d\theta Such that 0 \leq \theta \leq \frac{\pi}{2} and 0 \leq r \leq \sqrt{2} And evaluating this...

Homework Statement Use Green's theorem to compute the area of one petal of the 28-leafed rose defined by r = 5sin(14 \theta) Homework Equations A = \frac{1}{2} \int_c{x dy - y dx} \int \int_c{M_x + N_y}dx dy The Attempt at a Solution I'm really more confused about just what to do...

Homework Statement A pendulum consists of a particle of the mass m and a thread of the length l (we don't consider the threads mass). The acceleration caused by gravity is g. Solve the particles displacement and the force caused by the tension in the thread T in a polar coordinate system. The...

Homework Statement how can i convert this : - 2 (cos pai / 4 + i sin pai / 4 ) to Cartesian , Polar and Exponential form ? Homework Equations z = ( a + i b) The Attempt at a Solution r= -2 tan inverse = pai/4 / pai/4 ?? Thank you very much for helping me out

Express -2(cos pai/4+i sin pai/4 ) in Cartesian , Polar and Exponential form ? how can i convert this : - 2 (cos pai / 4 + i sin pai / 4 ) to Cartesian , Polar and Exponential form ? Thank you very much

Homework Statement using only trigonometric identities, derive the differential area element in polar coordinates? any help with this problem or at least a start? Homework Equations i found this so far dA=(dr)(rd θ) The Attempt at a Solution i have tried to figure this one out...

I came across this example on the net : We are integrating over the region that is the area inside of r = 3 + 2 sin θ and outside of r = 2, working in polar coordinates (r,θ). What is the limits of integration for θ? # I already know the answer. But I have no idea how to arrive at the...

Hi there, I am getting confused about how to work this out. I know that to convert cartesian coordinates to spherical coordinates you can use: theta=arccos(z) phi=arcsin(y/sin(theta)) my problem is that I have a list of coordinates, let's call them THETA and PHI. I change them into X,Y,Z...

Any web resources regarding changing the variable of integration from cartesian to polar coordinates that goes beyond the basic : x = r cos theta y = r sin theta r = sq rt (x^2 + y^2)I totally don't get how to find the limits of integration using polar coordinates and my undergrad textbooks...