Spherical Definition and 1000 Threads

Homework Statement find the volume between the cone z=√(x^2+y^2), and the plane z=14+x, above the disk x^2+y^2≤1, for the exact number Homework Equations r^2=x^2+y^2; The Attempt at a Solution I found x=z, for x^2+y^2≤1, for solve r^2≤1, so r≤1, or r≥-1. for θ,from0 to 2pi, but I...

Homework Statement find the volume between the cone x=√y^2+z^2, and the spherex^2+y^2+z^2=196 Homework Equations The Attempt at a Solution for x=√y^2+z^2, I got x^2=y^2+z^2, and 2x^2=196, x=98, for this, I don't know what i am supposed to do then. Thanks!

Homework Statement the volume v=(4/3)(pie symbol 3.14..)r of a spherical balloon changes with the radius a)at what rate does the volume change with respect to radius when r= 2ft? b) by approximately how much does the volume increase when the radius changes from 2 to 2.2ft? Homework...

I've no idea where to put this question but here it is I am trying to work through the examples our lecture has given in class and I wasn't getting them at all the first thing that confused me was \nabla . \underline{r} = 3 I tried this myself with \nabla . \underline{r} =...

I'm doing a Lagrangian problem in spherical coordinates, and I was unsure how to express the kinetic energy, so I looked it up and wiki states it should be this: http://en.wikipedia.org/wiki/Lagrangian#In_the_spherical_coordinate_system Which would give me the correct answer, but I'm...

Homework Statement See figure attached. Homework Equations The Attempt at a Solution See figure attached for the provided solution. I got everything up to what I put in a red box. Where does he get that negative from? Did he do that with the intentions of reversing the...

We have a sphere that its center of mass is not located in its center. suppose it has a mass of m. what we want to do here is to write its movement equations, using Newton's laws or lagranigian.by move ment we mean writing the equations if a) a force F acts on the body on a surface that is...

Hey guys I am trying to understand a code for a Fortran 77 subroutine which calculates spherical harmonics using the CERN library RASLGF for legendre functions. The code looks like this subroutine harmonics(max,theta,phi,Yr,Yi) implicit none integer max,k,nn,n,grens...

I know that a spherical lens does indeed have spherical aberration, and I know that this is caused by the marginal and axel rays of light converging at different points. My question is why? What is it about the lens that makes the rays incedent on the edges of the lens focus at a closer point...

Homework Statement Given that Lz(x+iy)m=m\hbar(x+iy)m. Show that L+=(x+iy)m. 2. The attempt at a solution I'm probably grasping at straws here, but when I see the expression for Lz I instantly go to Lz|lm>=m\hbar|lm>. This then leads me to suspect that |lm>=(x+iy)m. Is this correct...

This is really a continuation from another thread but will start here from scratch. Consider the case of a static thin spherical mass shell - outer radius rb, inner radius ra, and (rb-ra)/ra<< 1, and with gravitational radius rs<< r(shell). According to majority opinion at least, in GR the...

For electrostatics, I know that conductors have 0 electric field inside. And I know that the surface of a spherical conductor has equipotential, (Maybe this is true for all shape of conductor in equilibrium right? ). So my question is, is the potential 0 inside a conductor as well? Is it...

In another thread I posed basically the folowing problem: Take the case of a stationary, non-rotating thin spherical shell of uniform area mass density - outer radius rb, inner radius ra, with (rb-ra)/ra << 1. There is consensus opinion that everywhere exterior and down to rb, spacetime is that...

I am facing some problem about derivatives in spherical coordinates in spherical coordinates: x=r sinθ cos\phi y=r sinθ sin\phi z=r cosθ and r=\sqrt{x^{2}+y^{2}+z^{2}} θ=tan^{-1}\frac{\sqrt{x^{2}+y{2}}}{z} \phi=tan^{-1}\frac{y}{x} \frac{\partial x}{\partial r}=sinθ cos\phi then \frac{\partial...

Homework Statement The following equation describes a surface in spherical coordinates. θ =pi/4 Write the equation in the cartesian coordinates? that is, (r,θ,Ø) to (x,y,z) Homework Equations x=rsinθcosØ y=rsinθsinØ z=rcosθ r=sqrt(x^2+y^2+z^2) θ=cos^-1(z/r) Ø=tan^-1(y/x) The...

Basically, BB ammos were shot from an airsoft gun into a water filled tank. The experiment was recorded using a video camera. I can calculate the approximate instantaneous velocity of the bullet under water at a given time using Logger Pro. 1. Relevant equations Drag force = 0.5 ρAC0v2 2...

In the attached picture is all of the information to complete this problem. The picture is of a solid sphere at the center of a hallow sphere, both of which are conductors. The question asks to find the total charge of the exterior and interior surfaces of the hollow conductor, as well as the...

Homework Statement A spherical conductor of radius a is surrounded by a spherical conducting shell of radius b, and the gap is filled with an insulating material of resistivity ρ. A thin wire connects the inner surface of the shell to the surface of the conductive sphere, and a potential of...

So I have the following shape for which I want to calculate the inertia matrix. Basically I just want to know what limits of integration I should use if I am using spherical coordinates. Assume the convention that phi is the angle from x to y in the xy plane and theta is from z to the xy plane...

Homework Statement A top half of a spherical shell has radius R and uniform charge density sigma. Find the potential difference V(b)-V(a) between point b at the north pole, and point a at the center of the sphere. Homework Equations The Attempt at a Solution \oint E ds =...

Give a parametric representation of the following surfaces in terms of the given parameter variables: a) The first octant portion of the sphere (x^2) + (y^2) + (z^2) = 16 in terms of the spherical variables theta and phi. b)The graph of the function z = (x^3) - sqrt(y) in terms of the...

You are a hollow metallic sphere of inner radius r1, and outer radius r2. Inside is a charge of magnitude Q and a distance d<r1 from the centre. First I need to draw the electric field lines for regions r<r1, r1<r<r2, and r2<r Since the sphere is a conductor the only place where there is...

So here's the question: An ant crawls on the surface of a ball of radius b in such a manner that the ants motion is given in spherical coordinates by the equations: r = b, \phi = \omegat and \vartheta = \pi / 2 [1 + \frac{1}{4} cos (4\omegat). Find the speed as a function at time t and the...

Homework Statement I was trying to figure out how to derive acceleration in spherical coordinates, and I realized that I need to find the projection of each spherical unit vector [ e(r), e(θ), and e(φ)] onto each Cartesian unit vector [î, j, and k], but I'm not quite sure as to how to do that...

Homework Statement A solid sphere of radius R has a uniform charge density ρ and total charge Q. Derive an expression for its total electric potential energy. Suggestion: Imagine that the sphere is constructed by adding successive layers of concentric shells of charge dq = (4\pi r^{2} dr) ρ...

Homework Statement What is the dot product of two unit vectors in spherical coordinates?Homework Equations A∙B = ||A|| ||B|| cos(\theta) = cos(\theta)The Attempt at a Solution The above equation is the only relevant form of the dot product in terms of the angle \theta that I can find. However...

Homework Statement The potential inside a spherical shell is given by: V_{-}(x,y,z)= \frac{V_0}{R^2}(6z^2-3x^2-3y^2) P_n(\cos(\theta )) where \theta is the polar angle. The potential on the surface carries a surface charge density \sigma. Besides this, ther's no other charges and no outher...

Hi Guys, Suppose we have a spherical shell with charge density on the surface \sigma and radius R. The potential inside the shell is given by: V_(x,y,z) = \frac{V0}{R^{2}}(6z^2+ax^2+by^2) It is assumed, that the potential is rotational symmetric around the z-axis inside and outside the...

Hi, I seem to have forgotten some of my math how-to, as I haven't done this in a while. Looking through my notes, Bird, Stewart and Lightfoot, Greenberg, etc. don't really help. My equation is this, at steady state: 0 = 1/r^2 ∂/∂r (D*r^2 ∂C/∂r) + P Where P is some production rate...

Hi Guys, need some assistance. I am sure what I am asking is trivial but i still need help. How could i find the angle within a spherical triangle (triangle formed on a sphere). Now this triangle has equal lengths on all 3 sides. Pleas help!

What, "Physically" is a Spherical Harmonic? I'm trying to use spherical harmonics to get an equation to fit a set of data I have. I'm fine with that, I've found a derivation of what the general form is and I crunch that into MATLAB. My problem is derivations online really don't help me...

Homework Statement A conducting spherical shell that has zero net charge has an inner radius R1 and an outer radius R2. A postive point charge q is placed at the center of the cell. The 1st part was to find the electric fields at the 3 diff places. The part I need help on is where we have to...

Homework Statement A field is given in spherical coordinates as F=[cos(θ)/r2]∙ar+[sin(θ)/r]∙aθ. Express F in terms of x, y, z, ax, ay, azHomework Equations ar∙ax=sin(θ)cos(∅) ar∙ay=sin(θ)sin(∅) ar∙az=cos(θ) aθ∙ax=cos(θ)cos(∅) aθ∙ay=cos(θ)sin(∅) aθ∙az=-sin(θ) x=r*sin(θ)*cos(∅)...

1. Homework Statement [/b] A typical virus is a packet of protein and DNA (or RNA) and can be spherical in shape. The influenza A virus is a spherical virus that has a diameter of 85 nm. If the volume of saliva coughed onto you by your friend with the flu is 0.044 cm3 and 10−9 of that volume...

Homework Statement Prove that the spherical harmonic wave function \frac{1}{r}e^{i(kr-{\omega}t)} is a solution of the three-dimensional wave equation, where r = (x^2+y^2+z^2)^{\frac{1}{2}} . The proof is easier if spherical coordinates are used. Homework Equations Wave function...

Hello, in this diagram, the shaded regions are spherical conductors. What's the potential at A=B? Ignoring the outer sphere, it should be kQ/R. When you add the outer sphere, potential at C=D=0 and electric field between B and C is kQ/x^2 so i integrated (kQ/x^2) dx with interval [2R, R]...

I want to study antenna patterns of different arrangements. I am looking for a very cheap software ( free is even better) to plot graph if I provide the \;R,\theta,\phi. Even if 2D plot would be helpful like keeping either \;\theta\;\hbox { or }\; \phi\; constant and vary the other angle to...

So there are two concentric conducting spherical shells one with radius R and another 2R with charge +Q and +2Q respectively... Now the two are connected by a conducting wire. Why does the entire charge flow to the outer shell? Please clarify my doubts. I will be grateful.

I took the divergence of the function 1/r2\widehat{r} in spherical coordinate system and immediately got the answer as zero, but when I do it in cartesian coordiantes I get the answer as 5/r3. for \widehat{r} I used (xi+yj+zk)/(x2+y2+z2)1/2 what am i missing?

Hey, I've been stuck on this question for quite a while now: Homework Statement 1a. Write down an expression for the position vector r in spherical polar coordinates. 1b. Show that for any function g(r) of r only, where r = |r|, the result \nabla x [g(r)r] = 0 is true. Why does this...

Homework Statement Consider the study of the motion of a two bodies system interacting with only gravitational forces. If the two bodies (or even one of them) has not spherical symmetry, how will you proceed? Indeed the Earth and the moon does not have spherical symmetry mass distributions...

Homework Statement A concave spherical mirror has a radius of curvature of magnitude 27.1 cm. Determine the object position for which the resulting image is inverted and larger than the object by a factor of 4.00. Homework Equations Mirror equation in terms of focal length: 1/p + 1/q =...

Homework Statement A dentist uses a spherical mirror to examine a tooth. The tooth is 1.13 cm in front of the mirror, and the image is formed 10.8 cm behind the mirror. Determine the mirror's radius of curvature. Homework Equations 1/p+1/q=1/f f=R/2 The Attempt at a Solution...

Hi Here's the problem I am trying to do. a) Is the state \psi (\theta ,\phi)=e^{-3\imath \;\phi} \cos \theta an eigenfunction of \hat{A_{\phi}}=\partial / \partial \phi or of \hat{B_{\theta}}=\partial / \partial \theta ? b) Are \hat{A_{\phi}} \;\mbox{and} \;\hat{B_{\theta}}...

For my investigation regarding the aerodynamic forces on a spherical projectile, I really need to know the theoretical ratio of rotational kinetic energy to linear kinetic energy of a spherical projectile (assuming the only spin is forward spin and there is no Magnus effect). Can someone please...

Homework Statement f(x) is a differentiable function let F(t)= \int\int\int_{x^2+y^2+z^2\leq t^2} f(x^2+y^2+z^2) dx dy dz compute F^{'}(t) Homework Equations x=p sin \phi cos\theta y= p sin \phi sin\theta z= p cos \phi spherical bounds 0<p<t 0<\phi<\Pi 0<\theta < 2\Pi p^2...

I wanted to derive the volume of a sphere using triple integration with spherical coordinates, but instead of taking the limits of θ as (0° ≤ θ ≤ 180°), I chose to take (0° ≤ θ ≤ 360°), and therefore, for φ as (0° ≤ φ < 180°), Now of course the integral of sin(θ) from 0° to 360° is zero, and...

Homework Statement Using spherical coordinates, set up but DO NOT EVALUATE the triple integral of f(x,y,z) = x(x^2+y^2+z^2)^(-3/2) over the ball x^2 + y^2 + z^2 ≤ 16 where 2 ≤ z. Homework Equations x = ρ sin ϕ cos θ y = ρ sin ϕ sin θ z = ρ cos ϕ ρ^2 = x^2 + y^2 + z^2 ∫∫∫w...

Hello Everyone, I was just wondering if there was a way to add two vectors that are determined by spherical coordinates (radius, theta, phi). For example, if I have v1 = (5, Pi/4, Pi/2) and v2 = (3, Pi, -Pi/2) is there a way to add these using their respective radii, thetas, and phis or do I...

So I've been trying to derive the moment of inertia equation for a thin spherical shell and I've slammed into a dead end algebraically. I was able to derive an equation for a hollow sphere: I = (2/5) M (Ro^5 - Ri^5)/(Ro^3 - Ri^3) where Ro is the distance to the very outside of the sphere...