Radius Definition and 1000 Threads

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I don't understand the intuition/proof of why arc length = arc angle * radius. This may be partially because I don't fully understand the concept of radians, but anyhow please help.

A test tube filled with water is being spun around in an ultracentrifuge with angular velocity. The test tube is lying along a radius and the free surface of the water is at radius r(o). Show that the pressure at radius r within the test tube is: p = .5(p)(angular velocity)^2(r^(2)...

Homework Statement The monochromatic flux emitted from unit surface area of a black body is given by F_{\lambda}(T) = \frac{2h\pi c^{2}}{\lambda^{5}} \frac{1}{exp(hc/\lambda KT)-1} Wm^{-2}m^{-1} If the distance to star X is 620 parsecs, calculate: (a) the radius of star X, in...

Pretend that you are expaining the following to someone who knows nothing about complex numbers and within a universe where complex numbers have not been invented. In examining the function f(x) = \frac{1}{1 + x^2} we can derive the series expansion \sum_{n=0}^\infty (-1)^n x^{2n} We...

What is the physical significance of the radius of gyration

Homework Statement Consider the extreme case that the comet is released from rest at a distance R_max from the sun. In this case L is actually zero. Use the technique described in connection with 4.58 to find how long the comet takes to reach the sun. The radius of the sun for now is zero...

I am trying to find out a method of determining the area below a curve. The end points of the curve are known in cartesian space, and the curvature of the curve is known. A diagram of the curve is here, shown in the images belowthis webpage [SIZE="1"]ß must be in radians...

Prb:(x^4+4*x^2+16)y"+4(x-1)y'+6xy=0 P=(x^4+4*x^2+16) Q=4(x-1) R=6x P=0 for - 1 - 3^(1/2)*i 1 - 3^(1/2)*i - 1 + 3^(1/2)*i 1 + 3^(1/2)*i Q=0 for 1 R=0 for 0 Do we ignore Q & R, plotting P, then find shortest distance which would equal 2?

how to solve for mass given gravitational force and radius ? Homework Statement The gravitational force between two identical objects 2.00m apart is 3.50x10^-6N. determine the mass of each object. the answer should be [458kg] Homework Equations i know that Fg= GmM/r^2 so...

Hi everybody, Firstly sorry for my bad English . I have a question related to taylor series . I did not find easy way to solve it .Derivatives are becoming more and more complex . Please help me. question : Work out the taylor series of the function x/(1+x^2) at x =0 .Find the radius of...

Homework Statement We did an experiment using resistance putty and a multimeter. We changed the radius of the putty but kept the length the same. We recorded the resistances at different radius'. I know that physics theory says that resistance is inversely proportional to cross-sectional...

Homework Statement A particle of mass m moving in three dimensions is attracted to the origin by the gravitational force of a much heavier object. It can be shown that the radial motion is governed by the following equation m\ddot{r}=-\frac{k}{r^{2}}+\frac{l^{2}}{mr^{3}} where k is a...

Homework Statement The Schwartzchild radius for a black hole is the distance from the singularity of the black hole at which the escape velocity is the speed of light. You wish to create a black hole, with radius of only 1.0m for personal research. How much mass would this required? Would the...

do you consider Covalent radius, Van der Waals radius or atomic radius?

Homework Statement A non-conducting spherical shell is uniformly charged. The electrostatic potential \phi at the centre of the sphere is \phi1 = 200V The potential at distance r = 50cm from the centre is \phi2 = 40V Find the radius of sphere: a Homework Equations I seem to have...

Homework Statement the equation for the bohr radius is 4pi (permitivity of free space) * (reduced Planck constant)/ (elementrary charge)2(mass of an electron) The Attempt at a Solution let's just just focus on orders of magnitude: (10^-12 * 10^-34)/(((10^-19)^2)*(10^-31)...

Hello all I work in transport engineering. i have come across what seems to be a simple maths problem but i do not understand it. The problem relates to geometry i.e. calculating the radius of a curve using a chord and a versine. The problem is this:- " a general rule of thumb is as...

My friend and I were discussing particle accelerators (betatrons to be exact) and we began to argue about the size of the core magnets and vacuum chamber. He said that an average torodial vacuum chamber is 0.5m. I have seen old photos of them and said that's more likely to be the diameter. I...

A hydraulic steel tube of diameter 10mm and wall thickness 1.5mm has been bent to a radius of 100mm. Calculate the reverse radius of curvature that needs to be applied to straighten the tube. M/I= σ/Y = E/R I am really struggling on the above question. I think I need to read off the...

Radius of curvature and focal distance question? Hi everyone! Really struggling on these two questions and have spent way too many hours coming up with the wrong answers. Below are the questions and my attempts. Any help would be greatly appreciated! 1. Calculate the radius of curvature...

Homework Statement Using mass = 2.473x10^23kg and Density = 7.481g/cm^3 work out the radius of said sphere,Homework Equations D=M/V 4/3∏r^3 The Attempt at a Solution D=M/V DV=M V=M/D Mass = 2.473x10^23kg V=2.473x10^23kg / 7.481g/cm^3 V=2.473x10^23kg / 0.007481kg/cm^3 V= 3.31x10^24 cm V=...

Homework Statement A bowl has radius of 16 cm at the top of it (the largest diameter) and diameter of 8 cm at the bottom of it (the smallest diameter). Find the diameter at position: a. 1/4 height b. 1/2 height c. 3/4 height Homework Equations not sure, maybe: trigonometry...

Homework Statement Find the radius of convergence of the Taylor series at 0 of this function f(z) = \frac{e^{z}}{2cosz-1} Homework Equations The Attempt at a Solution Hi everyone, Here's what I've done so far: First, I tried to re-write it as a Laurent series to find...

Homework Statement At what distance along the central axis of a ring of radius R = 0.200 m and uniform charge is the magnitude of the electric field due to the ring's charge maximum? What is the positive solution for z? Homework Equations E = \frac{kqz}{(z^2+R^2)^(3/2)} The...

Homework Statement Find the radius of convergence of the Taylor series at z = 1 of the function: \frac{1}{e^{z}-1} Homework Equations The Attempt at a Solution Hi everyone, Here's what I've done so far. Multiply top and bottom by minus 1 to get: -1/(1-e^z) And then...

Okay, first of all, sorry for not posting here, I unknowingly posted this q in the wrong section and got an infraction. Sorry againHomework Statement Question : Calculate the change in gravitational potential energy of the moon, when the radius of it's orbit increases by 4cm. Radius ...

Hello. I have been going through some old OU books on the sciences and started working through an excercise when I came to a stumbling block. I have come here in the hope that someone may be able to shed some light on my problem. This is all for personal study as I am not enrolled on any...

What happens to bodies of mass as they approach and get near this value? If they don't actually reach the criteria, will their properties be vastly different from bodies that do reach the criteria? Will it expand instead of maintain it's radius? I'm also wondering how much energy it takes...

Homework Statement Snoopy is flying his vintage warplane in a "loop de loop" path being chased by the Red Baron. His instruments tell him the plane is level (at the bottom of the loop) and traveling at 180 km/hr. He is sitting on a set of bathroom scales that him he weighs four times what he...

Homework Statement An 80-kg pilot flies a plane in a vertical loop. At the top of the loop, where the plane is completely upside-down for an instant, the pilot hangs freely in the seat and does not push against the seat belt. The airspeed indicator reads the 110 m/s. What is the radius of...

I have a qualitative question to ask: The Schwarzschild radius of matter is proportional to its mass. The actual radius of the matter, assuming it is spherical, is proportional to the cube root of its mass. This implies that the density required to form a Schwarzschild radius decreases as...

Radius of convergence of the series n^2(x^n)/(3n!) I am stumped the question is: find the radius and interval of convergence of the following series {sum_(n=1)^(Infinity)}((n^2)(x^n))/(3*6*9***3n) I'm assuming that equal to ((n^2)(x^n))/(3n)! then lim_(n->infinity) of...

Homework Statement Neon is a monatomic gas; Density = 0.900 kg.m-3 Pressure = 1 atm Temperature = 273K. Density of liquid neon = 1207 kg.m-3 (i) Calculate the volume occupied by one gram mole of neon at a temperature of 273 K and a pressure of 1 atm. (ii) Determine the atomic...

Homework Statement A metal sphere of radius a is surrounded by a thick concentric metal shell (inner radius b, outer radius c). Neither the shell nor the sphere carries any charge, but there is a point charge +Q located inside an irregularly shaped cavity in the otherwise solid sphere as...

Homework Statement What is the radius of convergence of the Taylor Series of the function f(z) = z cot(z), at the point z = 0? Homework Equations Taylor series is given by: \sum_{k=0}^{\infty} \frac{f^{(k)}(z_{0})}{k!} (z - z_{0}) And the radius R by: \lim_{n \to \infty}...

Homework Statement Going over some old tests, I am asked to find the contour of the function: T = 100 - x^2 - y^2 at T = 100, T = 0, etc. I have a question regarding the contour at T = 100 Homework Equations The Attempt at a Solution Consider T = 100 100 = 100 - x^2...

Homework Statement an ball of mass m is connected by a string with spring constant k, to a rotating shaft. Find a relation between the radius of the circle, and the angular frequency. Homework Equations The Attempt at a Solution Let: Natural length of spring = x0...

Homework Statement What is the larmor radius of an electron in the inner van allen belt? This is for a General Astr class so I feel like I must be over complicating it. Electron Kinetic Energy in the inner VA belt: K≥30 [MeV] (much greater then its rest energy) VA Belt Radius: r~1.1-2.0...

An electron moves in a circular orbit of radius r in a magnetic field. The electron moves in a path perpendicular to the magnetic field. If the kinetic energy of the electron is doubled, what is the new radius of its path? What formula would I use to go about this? Is this about mass...

Homework Statement Ʃn!(x-1)n I need to find the radius of convergence for this summation from n=0 to n=∞ The Attempt at a Solution I started off with the ratio test: (n!(n+1)(x-1)(x-1)n)/(n!(x-1)n) = (n+1)(x-1) (x-1)lim(n+1)...Now at this point it looks to me like the series does...

Homework Statement You placed a 10cm high object in front of a mirror and got 5cm high virtual image at (-30cm). (Hint: watch the sign convention) a. Find the magnification b. Find the object distance from the mirror c. Find the radius of curvature of the mirror then I have to know if...

at what radius can you send peer-to-peer text messages / SMS over "ham radio"? suppose we have lots of people concentrated in a small area, like a college campus. Maybe a mile or so in diameter. We would like to set up a packet switched peer-to-peer SMS transmission using low cost long wave...

Homework Statement Suppose that the power series \sumanxn for n=0 to n=∞ has a radius of convergence R\in(0,∞). Find the radii of convergence of the series \sumanxn2 from n=0 to n=∞ and \sumanx2n.Homework Equations Radius of convergence theorem: R = 1/limsup|an|1/n is the radius of...

Homework Statement Suppose that the following series converges when x = -4 and diverges when x = 6. ∑{n=0 -> ∞} c_n • x^n What is the interval of convergence? The Attempt at a Solution I think it is [-5,5) but my friend reckons that it is [-5,6). I don't think [-5,6) is correct because this...

Is "radius" a misnomer in a polar equation? Often I see the description of "r" in a polar equation r = r(theta) as being "radius", but "radius" is a length, and here you can have a negative r. Hence "radius" is a misnomer, as far as I can tell. Perhaps it would be better described with some...

Hi, I have another query related to rolling motion. Lets say a disc is rolling purely with a velocity vo (this being the vcom). It encounters a step.lets say that the step has a height h, where h < r, i.e., the step has a height less than that of the height of the center of the disc. SO...

i see people discussing the convergence radius of a perturbation series in the literature i am really baffled generally, one can only get the first few coefficients of a perturbation series that is, the perturbation series is not known at all how can one determine the convergence...

Homework Statement Given the numerical value of a0= 5.3X10^11m in the Bohr hydrogen atom, find the radius of the first five orbitals as well as the radius for n=100. Homework Equations Rn=a0 x n^2 The Attempt at a Solution Could it be as simple as typing in for the third orbital...

two balls, one made of iron and one made of lead with same radius and mass. which one will roll down the slope faster? i don't really know where to begin, since everything is the same, the only idea i had was to somehow relate Ek=(J.ω2)/2 => Ek= m.r2.(ω2/2) to the question since i imagine...