Sphere Definition and 1000 Threads

There are plenty of proofs for the statement, but I do not find one which is not rely on other assumptions. Here are some common proofs of this statement: https://en.m.wikipedia.org/wiki/Great_Circle#Derivation_of_shortest_paths This proof require the path to be differentiable, which is not a...

Hi, Is there a way to derive the moment of inertia of a sphere without using the M of I of a cylinder? In other words, is it possible to find a sphere's from scratch? Please include a derivation in your answer, unless there isn't one of course.

Original Problem: "A sphere of radius a is made of a nonconducting material that has a uniform volume charge density [PLAIN]http://jkwiens.com/2007/10/24/answer-electric-field-of-a-nonconducting-sphere-with-a-spherical-cavity/d2606be4e0cd2c9a6179c8f2e3547a85_2.gif. A spherical cavity of...

Homework Statement The circumference of a sphere was measured to be 90 cm with a possible error of 0.5 cm. Use differentials to estimate the maximum error in the calculated volume. Homework Equations Volume of sphere: V=4/3πR3 Circumference of Sphere: C=2πR ΔC = 0.5 cm The Attempt at a...

Can it be defined a disfigured sphere to approximate a cube mathematically? 8 corners equilateral to some extent. Not exact.

Homework Statement Given a randomly drawn circle on a sphere, calculate the probability that it will pass within a defined distance of a set point. To make it clear, imagine the example of the the Earth and Mt Everest. What is the probability that a randomly drawn circle will come within, say...

Homework Statement A solid sphere of mass m and radius a can rotate freely about a point A on its surface. The sphere is held initially at rest with the line OA through A and the centre of the sphere O horizontal and is released under gravity. Find the angular velocity of the system when OA...

Homework Statement A small metal sphere X is charged by losing 500 electrons. An identical metal sphere Y is charged by gaining 1000 electrons. The two spheres are first put in contact with each other and then separated. If -e is the charge on an electron, what is the charge on each sphere...

I've been reading about how much of a sphere actually touches a flat plane (spheres are very interesting things, it turns out!). Mathematically, a perfect sphere has only one point of contact, meaning that the area of this contact is infinitely small(?), but as physicists, we know that there...

Homework Statement This is not really a school problem, it's actually something I am trying to figure out. So, we have a sphere with given radius. (Actually let's assume that all the parameters are known). The sphere has equally distributed heaters and is in the beginning at constant...

Since the pressure a sphere exerts on a surface tends to infinity, how do you actually calculate it? My guess would be trying to see how many atoms of the surface (a straight line) and of the sphere collide. But this is very dependent on the materials and exterior factors. I have searched...

If I have a square surface of 25 m^2 and I want to know how many sphere of radius r will cover 50% of the area, then how to proceed ? Should I calculate the area of circle which will form by projecting a sphere on a 2D surface, and divide 12.5 m^2 by this area to get the no. of spheres ?

Homework Statement Consider a sphere of radius ##R##, with a charge density ##\rho(r)=\frac{\alpha} {r^2},## with ##\alpha## a constant. Use Gauss' law to calculate the electric field outside the sphere at a distance ##r## from the sphere's centre (ie. ##(r > R)## and inside the sphere (ie...

Homework Statement A point charge q<0 lies just outside a uniformly and positively (non-conducting) charged ball. Assume the charge can pass through the ball freely. Describe the motion of the charge. Homework Equations Coulomb's force law, energy equation. The Attempt at a Solution Obviously...

Homework Statement Find the average velocity of shell while its moves a velocity v' and expands a velocity v. Sphere radius is R Expansion velocity v Movement velocity v' Homework Equations I think there's no need an equation.[/B] The Attempt at a Solution I try to find average velocity...

Lets think we have a sphere and it moves a constant veloctity v.So it will have a kinetic energy.Is this kinetic energy efectts spheres particle energy.(sphere made up but atoms) Thanks

Homework Statement Let a spherical object move through a fluid in R3. For slow velocities, assume Stokes’ equations apply. Take the point of view that the object is stationary and the fluid streams by. The setup for the boundary value problem is as follows: given U = (U, 0, 0), U constant, find...

just above the surface it's (kq/r^2) where r is the radius of the sphere and just below the surface it's zero, so is the electric field zero also exactly on the surface ? (as the q enclosed then will be zero since the flux is coming from the surface and not actually penetrating it) and...

i know it s zero because of the electrostatic equilibrium, but in terms of point charges : from the charge distribution on the sphere surface if we consider 2 point charges opposite to each other in direction : it s logical that at the point in the mid distance between them the electric field...

Hello All, Using Snell's Law, it is pretty obvious how to calculate the angle of refraction when both index of refractions are known. My question is how would I apply this to a 3 dimensional situation, such as light refraction in a sphere? Since there are two angles in relation to the normal...

Is an exact solution to Einstein's Field Equations known for the interior of a sphere of uniform density (to approximate a star or planet, for example?)

1. The problem statement, all variables and given/known my book says inside of a uniformly distributed sphere is zero and it also says it is not it is increasing. I didnt understand any single thing it is like kidding me? Homework EquationsThe Attempt at a Solution

Homework Statement A conducting sphere with radius R is charged to voltage V0 (relative to a point an infinite distance from the sphere where the potential is zero). What is the surface charge density σ? Express your answer in terms of the given quantities and ϵ0. Homework Equations Electric...

This is probably an elementary question, but I stumbled upon it while thinking about total differentials. One of their many applications is calculating the error in a volume, for example, given uncertainties in its dimensions. I'm not in the mood to tackle a 3D problem, so let's revert to a 2D...

Homework Statement Prove that an open sphere in \mathbb{R}^m is an open set. Homework EquationsThe Attempt at a SolutionTo show that an open sphere is an open set, any point inside the sphere has to be an interior point: Let us have a sphere B(P_0, r), r > 0, where P_0 is the centerpoint and r...

Can anyone explain to me why the following operators are rotation operators: \begin{align*}R_x(\theta) &= e^{-i\theta X/2}=\cos(\frac{\theta}{2})I-i\sin(\frac{\theta}{2})X= \left(\!\begin{array}{cc}\cos(\frac{\theta}{2}) & -i\sin(\frac{\theta}{2}) \\ -i\sin(\frac{\theta}{2})&...

This is an excerpt from "Introduction to Mechanics" by Kleppner and Kolenkow: "The reason why gravitational force vanishes inside a spherical shell can be seen by a simple argument due to Newton. Consider the two small mass elements marked out by a conical surface with its apex at ##m##. The...

Homework Statement Dear Mentors and PF helpers, I can do part (a) and (b) but don't really know how to do (c) and (d). Can somebody teach me how to go about solving it. Homework Equations Volume of cone: $$\frac{1}{3}πr^2h$$ Volume of cylinder: $$πr^2h$$ Volume of sphere...

hi, i'm a newbie... i have this problem: i have a sphere with known and constant R (obvious), i have two point with spherical coordinates P1=(R,p_1,t_1) and P0=(R, p_0, t_0) p_x = phi x = latitude x t_x = theta x =longitude x the distance between point is D=...

Homework Statement The system of 2 spheres is in equilibrium. Figure: . If the weight of the second sphere P2=20N, ABC=60 degrees and BAC=30 degrees, find the weight of the first P1 and the force that is applied on the drum of the pulley. Homework Equations P1=m*a The Attempt at a Solution...

Hi, I was hoping someone could help me figure out the problem below. It is a bit of a long winded questions so please bare with me! If you look at Fig 1 below, I have a sphere that spins about an axis in a clockwise direction. (the direction of the spin doesn't really matter) In this case the...

Hi, Basically I have a point cloud that represents balls with different radii. They are all moving based on forces and sometimes they are intersecting with each other. Imagine the yellow ball is going in one direction while the blue balls goes in another direction. At one time they are...

Homework Statement An insulated conducting sphere of radius ##R##, carrying a total charge of ##Q##, is in the field of a point charge ##q## of the same sign. Assume ##q\ll Q##. Calculate and plot the force exerted by the sphere on ##q## as a function of distance from the center. In particular...

This youtube clip has a ride that is a spinning sphere with objects hanging by strings from the surface. (see at about 0:55) This is the only ride in the video I think is theoretically impossible (the others seem like they could be done but would be dangerous and/or costly). I think it's...

Homework Statement What is the largest possible radius of a sphere which is inscribed in a regular tetrahedron a=10 ( this is the side of the tetrahedron) r=? r=5*√6/6 Homework EquationsThe Attempt at a Solution So first I calculated the Height of pyramid a2=(2/3*va)2+h2 h=√(a2-(2/3*a*√3/2)2)...

Homework Statement A charge conducting hollow sphere and a point charge with radius of sphere and distancestors between their centers Homework Equations [/B] 3. The atempt at a solution I am unable to find the potential of Shere in presence of external point charge

Homework Statement How do I prove that a sphere is a conductor? Homework Equations E = kQ/rThe Attempt at a Solution In my mind, if a sphere is a conductor, the charges formed during induction will move to the surface of the sphere as they can move freely in the conductor, and the same...

Homework Statement mass = M radius = r rot. inertia = i height = h Sphere of mass M is released from rest at the top of an inclined plane. The speed of the center of mass at the bottom of the incline, without friction, is sqrt(2gh). I need to find the velocity of the center of mass assuming...

Homework Statement A nonconducting sphere of radius r_2 contains a concentric spherical cavity of radius r_1. The material between r_1 and r_2 carries a uniform charge density rho_E(C/m^3). Determine the electric potential V, relative to V=0 at r= infinity, as a function of the distance r from...

Homework Statement I was looking for some practice problems in my textbook and found this problem that I was just a little stuck on. I drew the diagram from my textbook with the givens of the problem. Homework Equations ∲E*dA = Q (inside) / ɛ0 The Attempt at a Solution For r less...

Homework Statement A falling sphere viscometer measures the viscosity of a liquid from the terminal velocity of a tiny, falling sphere. One such device determines that a tiny sphere of radius 46 μm falls through a liquid with a terminal velocity of 2.5 mm/s. If the density of the sphere is 4171...

Homework Statement Find the moment of inertia of a solid sphere of uniform mass density (like a billiard ball) about an axis through its center Homework Equations I = ∫rρdV The Attempt at a Solution I =ρ ∫r4πr2dr = ρ4π∫r4 Then I integrate this from 0 (the center) to R, so I = (ρ4π)*(R5/5) And...

Homework Statement Using an electron as a point particle of charge −e inside a positively charged sphere of radius R ≈ 10^(−10) m and total charge +e, find the density ρ(r) of the positive charge for which the electron oscillates harmonically about the center of the sphere assuming that the...

Homework Statement An uncharged nonconductive hollow sphere of radius 12.0 cm surrounds a 11.0 µC charge located at the origin of a cartesian coordinate system. A drill with a radius of 1.00 mm is aligned along the z axis, and a hole is drilled in the sphere. Calculate the electric flux through...

Homework Statement A point charge q1 = -6.1 μC is located at the center of a thick conducting shell of inner radius a = 2.8 cm and outer radius b = 4.8 cm, The conducting shell has a net charge of q2 = 2.6 μC. Homework Equations E = (kQ)/r2 F = (kq1q2)/r2 The Attempt at a Solution I honestly...

Homework Statement Three fixed point charges of +2 nC, −3 nC and +4 nC are located inside a thin uncharged metal spherical shell of radius R = 2 cm, as shown in the picture attached. Calculate the strength and direction of the electric field at position P, being 10 cm from the centre of the...

Homework Statement A non-conducting sphere of radius R has volume charge density ρ = B/r. for r<R and ρ = - for r>R. B is a constant. a) Calculate E-field for r>R. b) Calculate E-field for r<R. c) Calculate potential for r>R. d) Calculate potential for r=R. e) Calculate potential for r<R...

Homework Statement Find an equation of the largest sphere with center (5, 4, 9) that is contained in the first octant. Homework Equations x2 + y2 + z2 The Attempt at a Solution [/B] (x - 5)2 + (y - 4)2 + (z - 9)2 = R2 I am under the impression that R must be no greater than 4, is this...

Homework Statement An expanding sphere, radius ##R(t) = vt## (##t>0##, constant ##v##) carries a charge ##Q##, uniformly distributed over its volume. Evaluate the integral Q_{eff} = \int \rho(\vec{r},t_r) d\tau with respect to the center. (##t_r## is the retarded time and ##d\tau## is an...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >[/color] So the problem that I have been assigned has formulas of rotational energy, momentum, trajectories, inertia, and inclined planes. A solid sphere is rolling down an inclined plane (that is...