Cylindrical Definition and 761 Threads

I'm having some trouble understanding exactly how to graph this problem using cylindrical coordinates. The coordinates they give me is r=2cos(theta) How do I go about beginning to determine how to graph this with only the radius?

Use cylindrical shells to calculate the volume of the solid obtained by rotating the region bounded by y=x and y=x^2-2x about the line y=3 I know how do set the problem up and how to do it, I just don't know how to write "y=x^2-2x" in terms of "x". This is how I think the problem should be set...

Use the method of cylindrical shells to find the volume of the solid generated by revolving aabout the indicated axis the region bounded by the given curves. x=y, x+2y=3, y=0; about the x axis. Latest version of my work: (I don't know how to paste a graph into the post. But I graphed my...

Water is flowing down a cylindrical pipe of radius r. (a) Write a formula for the volume, V, of water that emerges from the end of the pipe in one second if the water is flowing at a rate of (i) 3 cm/sec (ii) k cm/sec (b) Graph your answer to part (a)(ii) as a...

Please help! How do I do this problem? Using the method of cylindrical shells, find the volume generated by rotating the region the region bounded by the given curves about the specified axis. y=(x-1)^(1/2), y=0, x=5; about y = 3 Please tell me how to set up the integral! Any help is...

find volume: y=x^2, y=0, x=1, x=2 about x=1 I found the height to be x^2 and circumference to be 2pi(1-x) So V= \int_1^2 2\pi(1-x)(x^2)dx This is not giving me the right answer.

Hey I am given the set volume for a cylindrical container and separating pricing for the material used to construct the container, the base and the side wall. The ends of the container cost $0.05 per cm2 and the side walls $0.04 cm2, and the volume is 400 mL. The question asks: What is the best...

Hello. I am interested in learning the mathematical derivation from Cartesian coordinates Navier-Stokes equation to cylindrical coordinates Navier-Stokes equation. These equations have similar forms to the basic heat and mass transfer differential governing equations. I’ve tried looking...

Sir, A driving mirror consists of a cylindrical mirror of radius 10 cm and the length over the curved surface is 10 cm. If the of the driver be assumed to be at a great distance from the mirror, what is the field of view of the mirror in radian? I don’t have any idea about cylindrical...

Hi everybody, didn't really know where to put this thread since it's physics using math, so I'm sorry if it's not in its appropriate place. My problem is: I need to compute the mass of oil in a cylindrical core put into a core holder.it's partially filled of oil. I didn't know how to...

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. y = x^2 y = 4 x = 0 0 <= x <= 2 So I drew these: http://img131.imageshack.us/img131/9225/math28qi.th.jpg...

I would like to know about fine tuning of an airplane Fuel Gauging probe. It is basically a cylindrical capacitor made of an inner composite tube of about 0.5 inch diameter and an outer composite tube of about 1 inch diameter. The length of the tubes varies from about 3 inches to 8 inches. The...

We just started a section dealing with div/curl/grad in different orthogonal systems... before I get started doing problems involving these operations I wanted to make sure I am dealing with these operation correctly. Our first homework problem is as follows: In cylindrical coordinates compute...

Hi =) I was given this problem on a test: a vector A = 2yi - Zj +3xk, was given in rectangular (cartesian) coordinates and I had to convert it to cylindrical coords. What I did to solve it was this: 1) A = 2rsin(theta)i - zj + 3rcos(theta)k 2) partial derivatives a) d/dr =...

Hey everyone, I have failed to show that the magnetic flux outside a cylindrical conductor is zero. The problem goes like this: a coaxial cable consists of a solid inner cylindrical conductor of radius a and an outer cylindrical conductor of inner and outer radius b and c. Distributed...

Hi , I don't know how to get the edge of the cone in cylindrical coordinates. For example, we have a cone starting at the origin, of heigth 2 and the top is a circle of radius 1 (center at the origin). the edge of the cone is z=2r. but I don't know how they find it. Please can someone...

Can someone, please, show me an example of when you are better of with parabolic cylindrical coordinates than with cartesian coordinates when computing a triple integral over a solid?

Prove that any cylindrical can of volume K cubic units that is to be made using a minimum of material must have the height equal to the diameter.

I'm supposed to prove the laplacian in cylindrical coord. is what it is. I tried tackling the problem in two ways and none work! I have no idea what's the matter. The first way is to calculate d²f/dr² , d²f/dO² and d²f/dz² and isolate d²f/dx² , d²f/dy² and d²f/dz². In cylindrical coord...

I have this question on this article by G.K. O'Neill,1974. who proposed having a cylindrical habitat in space. Then the article posed a question asking me to ponder on the speed of the rotation of the cylinder such that it wld imitate Earth's gravitational field at the walls of the cylinder...

I have this question on this article by G.K. O'Neill,1974. who proposed having a cylindrical habitat in space. Then the article posed a question asking me to ponder on the speed of the rotation of the cylinder such that it wld imitate Earth's gravitational field at the walls of the cylinder...

Hi to you all.i have an exercise i cannot solve.i think something is missing. Cylindrical tube V=10L opened at the top has air with a temperature of T1=27 oC.We provide heat to the tube until the temperature reaches the value of T2=327 oC.A)we have to find the amount of air that leaves from...

I have a question about the equation mechanics of cylindrical and spherical coordinate systems This is basically about the velocity and acceleration equations of both Let me just give an example from cylindrical \vec v = \dot r\hat e_r + r\dot\theta\hat e_\theta + \dot z\hat k and...

I don't understand this problem. I think it is difficult for me. Please anyone suggestion this problem to me. Thanf you Let us cosider steady state heat transfer problem in which laplaceT(r)=0 What is the temparature at the center of a thin disc of radius a whose average boundary...

Two long, charged, thin-walled, concentric cylindrical shells have radii of 3.0 and 6.0cm. The charge per unit length is 5.0x10^-6 C/m on the inner shell and -7.0x10^-6 C/m on the outer shell. What are the magnitude E and direction radially inward or outward? I figured I could use the...

Hi I'm stuck on an integration problem where I need to use the method of cylindrical shells to calculate a volume. Q. Using the method of cylindrical shells, find the volume generated when the area bounded by the curve y = x^2 - 3 and the line y = 2x is revolved about the line x = 7. The...

The capacitance measurements of “Fuel Gauging Tubes” (FGT) that are composed of carbon composite inner and outer tubes shows unacceptable level of variations and I need to reduce the variation of capacitance. I would like to know what are the contributing factors to capacitance variations...

I'm having trouble with solving this problem: Suppose we have a cylindrical brick chimney with height L. It starts to topple over, rotating rigidly about its base until it breaks. Show that it is most likely to break a distance L/3 from the base because the torque is too great. So I'm...

This gigantic thing here called the Centauri Princess, can it be built in the next few hundred years? http://www.astroscience.org/abdul-ahad/firstarktoalphacentauri.htm That would be the greatest engineering achievement in all human history...

I know one can figure the volume of a torus by the difference of two volumes, but I'm trying out the method of cylinderical shells. As far as i understand, you can often create a primitive with a calcuable volume and approximate the volume of the shape you wish by scaling the primitive along the...

How can you derive the gradient of a vector R^3 to R in cylindrical coordinates?

Could anyone please help me with the following problem? [FONT=Courier New]A compact package contains n = 100 long straight wires, shaped like a cylinder with a radius of R = 0.500 cm. If each wire conducts i = 2.00 A, calculate the intensity and direction of the magnetic force per unit of...

Hey, I have a question on a derivation The following is in my textbook (V = vector): \nabla \cdot V = \frac {1}{r} \frac {\partial{(rV_{r}})}{\partial{r}} + \frac {1}{r} \frac {\partial{V_{\theta}}}{\partial{\theta}} + \frac {\partial{V_{z}}}{\partial{z}} where: \nabla = \hat {r}...

I'm having trouble figuring out this volume. Use the cylindrical coordinates to find the volume of the solid S bounded by z=x^2 + y^2 and z=12 - 2x^2 - 2y^2 I've included a pic of what I think the regions and the solid look like...

I have this flow field in cylindrical coordinates of which I would like to calculate the dissipation as a function of these coordinates. Now in my fluid dynamics notes I found the following expression(s) for the dissipation: 2 \mu (e_{ij} -\frac{1}{3} \Delta \delta _{ij} )^2 = 2 \mu (...

My notes have an example of verifying the divergence theorem using cylindrical polars. There's a vector field, A(r) = x(x-hat) + y(y-hat) + z^2(z-hat) and my notes say: "Note that rho-hat = cos phi(x-hat) + sin phi(y-hat) and phi-hat = -sin phi(x-hat) + cos phi(y-hat) and so A(r) =...

The problem says to find the volume of material cut from the solid sphere, r^2 + z^2 \le 9 by the cylinder, r = 3\sin\theta I don't know how to graph the first equation, but I can do the second in polar coordinates. How do I go about converting to use cylindrical coordinates?

I have a thick cylindrical wire that I make it 10 smaller pieces and the area remains constant. How do I find the toatal current at 60 Hz? given sigma, miou, and radious I also need to find the total current for a given maximum current density that was given for the thick wire for AC. How to...

For some reason, I am having a lot of difficulty finding the electric field between two co-axial cylinders. In fact, I pretty much know that it should be: \frac{Q}{2\pi \epsilon _0 Lr} Where Q and -Q are the charges on the two cylinders, L is the length of the cylinders, and r is the...

I find this passage \frac{\partial}{\partial x} = \cos(\phi)\frac{\partial}{\partial \rho } - \frac{\sin(\phi)}{\rho}\frac{\partial}{\partial \phi} difficult to understand. My teacher wrote this as an explanation: \frac{\partial V}{\partial x} = \frac{\partial\rho}{\partial...

How do I get the bounds for a function w/out drawing a graph?? Like, Volume of the solid bounded above by the sphere r^2+z^2=5 and below by the paraboloid r^2=4z. How would I get the bounds for these in cylindrical coordinate (r dz dr dtheta)? ***Mass of the solid inside the sphere p=b and...

"simple" shell I know this is relatively simple, but I'm a little rusty. Could someone help me out? We want to find the volume of the solid obtained by rotating the region bounded by the curves y=x^4 and y=1 about the line y=7 using the cylindrical shell method. According to my book the...

is it leagal to define a vector with respect to the orgin in cylindrical coords? can a position vector to a point such as...(a, pi/4, pi/3) can u define a position vector <a, pi/4, pi/3>_o, o = (0,0,0)?

Anyone trying this experiment? Put a solid cylindrical electrode (anode/cathode) inside a hollow cylindrical or tightly coiled electrode (cathode/ anode) so that there is only a minimal ‘potential space’ between the two electrodes, and immerse them in a suitable electrolyte solution. The...

a flute is cylindrical and when you hit the 2nd register (higher notes) the fingering is pretty much the same as on the base register. in other words, the jump is a regular octave. a clarinet is conical and the jump to the 2nd register is a 12 note jump from what i understand. can anyone...

Hi, I was hoping someone could check my work on a few problems and get me started on a few others. It involves definite integration, so I'm going to use (a,b)S as an integration symbol and P for pi. These are the ones I need checked: 1. Use cylindrical shells to find the volume of the...

I'm stuck on two problems. I hope someone can help me. Here they are... 1) For 1a I thought Q would be Q=\rho \pi L (b^2-a^2) but since \rho=\frac{k}{r} so Q=\frac {k \pi L (b^2-a^2)}{r}. After being stumped on 1a I'm not sure how to go about 1b. 2) I've derived about 4 equations for this...

Question: (Note: p=rho and o=phi) Convert p(1-2cos^2(o))=-psin^2(o) into cylindrical and rectangular coordinates and describe or sketch the surface. The part that I don't know how to do is converting the spherical equation into cylindrical or rectangular coordinates. I know all the...

Question: (Note: p=rho and o=phi) Convert p(1-2cos^2(o))=-psin^2(o) into cylindrical and rectangular coordinates and describe or sketch the surface. The part that I don't know how to do is converting the spherical equation into cylindrical or rectangular coordinates. I know all the...

Problem : A long coaxial cable carries a uniform volume charge density \rho on the inner cylinder (radius a ), and a uniform surface charge density on the outer cylindrical shell (radius b ). The surface charge is negative and of just the right magnitude so that the cable as a whole is...