Sphere Definition and 1000 Threads

Homework Statement Calculate the moment of inertia of a uniformly distributed sphere about an axis through its center. Homework Equations I know that $$I= \frac{2}{5} M R^{2},$$ where ##M## is the mass and ##R## is the radius of the sphere. However, for some reason, when I do this...

Homework Statement A sphere of radius R carries a polarization of \vec{P} = k \vec{r}, where k is a constant and \vec{r} is the vector from the center. Find the bopund charges, and the field inside and outside the sphere Homework Equations - \nabla \cdot \vec{P} \sigma _b = \vec{P} \cdot...

How do you prove that for a given volume, sphere has the minimum surface area?

Hi , one of my electric field and how it works questions. My friend made a drawing that will help you visualize what i mean better. So we have a sphere made from wire or metal beams etc doesn't matter.Now we wrap wire around it and leave the ends separate, we attach a circuit of a resistor...

If I take two arbitrary continuous maps ##f,g:S^n\rightarrow S^n## such that ##f(x) \neq -g(x)## for any ##x\in S^n##, then ##f## and ##g## are homotopic. How do I show this result? I really don't see how to use the condition that ##f## and ##g## never occupy two antipodal points. Any hint...

So, I have been trying to figure out how to derive the equation for the surface area of a sphere. All attempts have resulted in colossal failure and as such are not even worth posting on the forum. I know Archimedes was the first to come up with the formula but I have not been able to find...

the formula for the surface area of a sphere is SA = 4 (pi) r2, with pi = 22/7 and r = radius of the sphere. for example the SA for Earth with a radius of 6,378 km is 510,065,600 km2 what would the radius be in order that for you to lay a grid of perfect square on the surface of the sphere?

According to the theories that discuss gravity, if humans were to create a solid metal sphere with the same mass as Earth would it have the same gravity as earth? Would it have to be orbiting something and/or moving to have that same gravity? Or could it be stationary and have the same...

If there is a rotating sphere (falling through a fluid) a) is the torque the same at every point on the sphere's surface, and b) how would I use said torque to work out the pressure exerted by opposite 'sides' of the sphere on the fluid? Homework Equations The Attempt at a Solution

Homework Statement A light ray parallel to the x-axis strikes the outer reflecting surface of a sphere at a point (2,2,0). Its center is at the point (0,0,-1). The unit vector along the direction of reflected ray is ##x\hat{i}+y\hat{j}+z\hat{k}##. Find the value of ##yz/x^2##. Homework...

Homework Statement Two large , horizontal charged plates are separated by 0.050m. A small plstic sphere is stationary and suspended between them and is experiencing an electric force of 4.5x10^-15 N. What is the mass of the sphere? F=ma My attempt. F=4.5x10^-15N a=9.8m/s^2...

Homework Statement A hollow spherical conducting shell is suspended in air by an insulating string, so that the sphere is electrically isolated. The total charge on the conductor is -6 μC. If an additional point charge of +2μC is placed in the hollow region inside the shell, what is the total...

Homework Statement Show that the volume of a sphere of radius r is V = (4/3)πr^2 Homework Equations calculus, integration The Attempt at a Solution I have the solution in the book but it's confusing me, I'll attach a picture. So I get lost where it starts talking about...

Hi guys, This is my first post here, this place looks like a great resource. Well, jumping straight in, I have a couple of questions on diffusion. At work, I did a couple of experiments with Ion Exchange Resins. Not getting the results we wanted, my boss asked me to do an analysis of...

So, I'm to show that in spherical coordinates, the length of a given path on a sphere of radius R is given by: L= R\int_{\theta_1}^{\theta_2} \sqrt{1+\sin^2(\theta) \phi'^2(\theta)}d\theta, where it is assumed \phi(\theta), and start coordinates are (\theta_1,\phi_1) and (\theta_2, \phi_2)...

Hi all, it might be a silly question, but my math is "a bit" rusty. I want to find the equation of the volume lost during the dissolution of a sphere particle as function of time: A=area of sphere V=volume of sphere t=time k=dissolution rate as volume dissolved over area time...

A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls, U-Unchanged), when that...

Homework Statement Hi, I'm trying to find the potential of conducting grounded sphere with radius Rs which located in the center of charged ring with Rr (>Rs) with charge density λ, h meters up to the z axis (see the attached images) Rs=4.3[cm] Rr=6.6[cm] h=13.1[cm] λ=1.0[esu/cm]...

I'm trying to wrap my head around how a rolling and slipping sphere would be behave on an incline (with an angle of θ) that is too steep for pure rolling. I believe I understand the behaviour up to that point but once we reach the position where the amount of friction required to maintain...

Hello all, I am attempting to simulate collisions of pool balls. For the moment i am doing so without taking rotational momentum or friction between balls into account. right now i have a system that successfully simulates a collision between 1 ball and another ball. Here's how it basically...

A sphere of mass 'm' collides with a fixed plane with initial speed 'u' at an angle 'α'(alpha). The sphere rebounds with speed 'v' at an angle 'β' with the normal. The plane being fixed remains at rest. We applied Newton's Experimental law( along the common normal(CN) The equation after...

Hi, One of the boundary conditions when solving for the potential, \Phi, outside a dielectric sphere placed within a uniform electric field is \lim_{r→0}\Phi(r,θ)<\infty Can anyone explain/prove why this so. Thanks,

θHomework Statement The attached diagram depicts a sphere with several variables: the height of the cylinder, the radius of the cylinder and an angle. All that has been given to me is the hypotenuse of a triangle used. Homework Equations To my knowledge I was told to use 2sinθcosθ=sin2θ...

Homework Statement I know how to find the volume of a sphere just by adding the areas of circles, so I decided to do a double integral to find the same volume, just for fun. Here's what I've set up. I put 8 out front and designed the integrals to find an eighth of a sphere that has its center...

I was doing some simple physics with a ball resting on a table and I made this curve (0,0) (25, 6.8) (50, 27.51) (75, 63.4) (100, 112.34) (125, 175.7) (150, 253.3) (175, 345.4) I was wondering if anyone could identify what sort of curve it is? I am just curious. This is not a homework...

Hello, I'm having trouble with a conduction problem, I have access to the answer but not the solution. I did it on my own and my value is half of what the answer is. Now, my calculus is a little rusty, but I don't know where I am going wrong. So the dimensions and temperatures of the sphere...

I am looking for the derivation to an approximation formula for the differential cross section for hard sphere scattering in the limit of high energy. The paper that mentioned this had referred to Methods of Theoretical Physics, PM Morse and H. Feshbach page 1484 but I have no access to the...

Homework Statement Check that the volume of a sphere is 4/3(pi)r^3 (use disk method) So I don't understand it I got stuck so I looked. I still don't get their solution. Chapter 7, section 2, question 59. http://www.calcchat.com/book/Calculus-ETF-5e/ Homework Equations The...

Homework Statement An insulating sphere of radius 0.240 has uniform charge density 6.50×10−9 . A small object that can be treated as a point charge is released from rest just outside the surface of the sphere. The small object has positive charge 4.10×10−6 How much work does the electric...

Hi, I'm trying to understand the mass conservation equation for a pulsating sphere which has thickness dr. Please refer to the attached solution. \rho = \rho_{0} (ambient density) + \rho' (small deviation) There are two things I don't follow. First, is that to obtain the mass, the area of...

Homework Statement Show that the circle that is the intersection of the plane x + y + z = 0 and the sphere x2 + y2 + z2 = 1 can be expressed as: x(t) = [cos(t)-sqrt(3)sin(t)]/sqrt(6) y(t) = [cos(t)+sqrt(3)sin(t)]/sqrt(6) z(t) = -[2cos(t)]/sqrt(6) Homework Equations The...

In my Physics book there was this problem of finding electric field produced by the sphere, such that electric charge is distributed uniformly throughout the volume of an insulating sphere. I know that excess charge tends to distribute itself on the surfaces, but since this sphere is made...

Coriolis effect - In a non-friction system, f I roll something along the surface of the planet from on of the poles to the equator, it will appear to move to the west, it will essentially stay behind the planets rotation and actually rotate it in the opposite direction. Now, if we add friction...

Homework Statement Homework Equations The Attempt at a Solution The ground is at zero potential. Hence, the sphere should be also at zero potential. The net charge should be zero, so a charge of -Q should flow from the ground to sphere. But this is wrong. :confused:

I want to know why everything in the universe forms a Ball or Sphere? Is gravity the cause of this? If so why? For example, If we were to pick the sphere apart can we see the source of gravity? Is gravity also a ball or sphere and can we grasp and see it? Why do we not ever see square planets or...

Homework Statement Consider the unit sphere x^{2} + y^{2} + z^{2} = 1 Find the volume of the two pieces of the sphere when the sphere is cut by a plane at z=a.The Attempt at a Solution My interpretation is that a is a point on the z-axis that the plane cuts at. So the height of the segment...

An alternate one by the by. My approach will be working with a base ten logarithm function(s). I'm going to graph the sphere on a 3d graph. I'm going to give the value of the radius, one unit. I will first look at the ten elevations up and down from the index, establish the area at each...

On the surface of a sphere, we can find the radius of cuvature of the sphere by: angle excess / area = 1/ r_s^2 http://en.wikipedia.org/w/index.php?title=Angle_excess&oldid=543583039 If we use triangles, for instance, the angle excess is the sum of the angles of the triangle minus 180...

Got a little problem here, just want to make sure what I'm doing is right because it's a little different from anything I've done that is using the same formula initially. So there's a sphere denoted as \(\Omega\): $$x^2+y^2+z^2=R^2$$ and its cut by two planes \(z=a\) & \(z=b\) where...

A spherical conducting shell with charge total q surrounds a charge –2q at the center of the shell. The charges on the inner and outer surfaces of the shell are respectively I know that if the conducting sphere has no charge the inner and outer charges would be +2q, and -2q respectively but...

Homework Statement As of the past few hours I've been trying to make sense one how to calculate the velocity of a sphere that moves down a frictionless ramp. My biggest problem with this seems to be that I'm confusing myself with the linear velocity and the angular velocity. Note that the...

I am curious about the relationship between an ever expanding sphere's radius and its surface area. how would I relate the rate of change in radius to the rate of change in the surface area.

What I understand is this: Shell theorem states that the force of gravity is focused at the center of an object. But, say that there is a large planet with a gravitational force equal to that of earth's. It is perfectly round… and hollow. Since it is hollow, how large would it be to have Earth's...

how can I create a spheric glass ball or a closed cylinder containing a solvent as acetone or methanol? the ideal would be without air bubble inside and diameter in the range of 2-4 mm thanx max

Instead of the shell method, can't one find the volume of a sphere by integrating/summing its horizontal areas?

I am in general physics III (E&M) at Cal Poly and I have a midterm tomorrow... my professor didn't go over Gauss' Law too much, so I'm having issues with this problem that is on his review. I will write the question exactly as it appears on the sheet. Homework Statement "You have a hollow...

Homework Statement I'm trying to figure out an equation for finding the net flux that abandons the surface of a sphere which contains a line charge distribution an a charge density. The problem is: A line charge distribution of 0.6m long with a charge density equal to 5C/m, is contained...

Homework Statement A sphere with radius .175 cm has a density ρ that decreases with distance r from the center of the sphere according to ρ= ((2.75*10^3) kg/m^3) - ((9.25*10^3) kg/m^4)r A) Calculate the total mass of the sphere. B) Calculate the moment of inertia for an axis along...

Homework Statement Given a uniform sphere of mass M and radius R. Use integral calculus and start with a mass dm in the sphere. Calculate the work done to bring in the remainder of the mass from infinity. By this technique show that the self-potential energy of the mass is: P =...

Homework Statement A sphere magnet of radius a has permanent uniform magnetization, z-axis. So we were trying to find the magnetic field at the center of the magnet in class. Homework Equations j_M(θ)=Msin(θ) dI=j_M(θ)adθ circular loop r_{loop}=asin(θ)The Attempt at a Solution When using...