Radius Definition and 1000 Threads

Homework Statement: Derive the formula for moment of inertia of a hollow sphere. Homework Equations: Required answer ##\frac{2MR^2}{3}## Consider a Hollow sphere. At an angle ##Θ## with the vertical, consider a circular ring whose moment of inertia is given by ##MR^2##. The most basic...

Well, what I've done so far is calculating the magnitude of velocity and acceleration replacing ##t=2## in ##\theta (t)## and ##r(t)## so I could get the expressions for ##\dot r##, ##\dot \theta##, ##\ddot r## and ##\ddot \theta##. But that's not my problem... my problem is related to the...

I can calculate the angular speed but I don't know how to calculate the radius. Is there certain formula to calculate it? Thanks

In order to calculate for the curl of the induced electric field for a loop moving in a uniform magnetic field, and using the cylindrical coordinate system for a curl, it's my understanding that since the B field is in the 𝑧̂ direction, then so is the partial time derivative of B, and therefore...

I had created a formula on arc of a circle...How can I publish it ..So that people see it and decide is it important or not.

Middle point of (1,3)(2,4) is (1.5, 3.5) r1 to r2 passing through (1.5, 3.5) I cannot grasp on what should i do to find r1 and r2 from the line Without graph*

Suppose a sphere were to be placed around our Sun with a radius equal to the radius of the orbit of Earth, it would have a volume of 6.266x1022 m3. At any instant in time there would be 3.846x1027 Watts of energy within this volume in the form of photons from the Sun. Since...

A singularity would be: a location in spacetime where the gravitational field of a celestial body is predicted to become infinite by general relativity in a way that does not depend on the coordinate system. (wiki) If the threshold to get a singularity is reached then space-time curvature...

Hello! I am a bit confused about the definition of the radius in Schwarzschild metric. In the Schutz book on GR (pg. 264, General rules for integrating the equations) he says: "A tiny sphere of radius ##r = \epsilon## has circumference ##2\pi\epsilon##, and proper radius...

In chapter 10 (Radiation; just after example 2 from 'Radiation from an arbitrary source') of Introduction to Electrodynamics by G. Griffiths he asserts that a charged sphere with oscillating radius doesn't radiate because, by Gauss law, ##E## stays the same no matter where the charges are...

I was wondering how one can calculate the radius of the circle a car will follow if it turns its wheels a given angle to its current velocity? For example, if i turn the wheels of my car by 12 degrees to my current direction, how large of a circle will the car perform

Imagine a container with compressed air ruptures. Inside is a metric ton of air, just very dense. If it explodes, ignoring fragments of the container and the ground, how would i calculate the blast radius? Do I need the Volume of the container or the density? I thought it might just be the...

I have found plenty of information about the radio source Hercules A. Its large radio jets are 1.5 million light years long from end to end, the supermassive black hole that produces Hercules A is 3 to 4 billion solar masses, and the black hole exists in the center of galaxy 3C 348. However, I...

I have tried a lot by angle chasing e.g. let ∠ABC=x° then ∠ACB=90°-x°. As AU=AV=radius of circle so ∠AUV=∠AVU=45°. I've connected U,D and V,D. Then ∠UDV=135° etc. But I haven't found any way to get near of proving AE=DE. I have also tried to prove 'the area of triangle AEU= area of triangle...

Find Radius and Interval of Convergence for \sum_{1}^{\infty}(\frac{x}{sinn})^{n}. I don`t have any ideas how to do that :/

I am starting to learn classical physics for my own. One exercise was, to calculate the vector r (see picture: 1.47 b). The vector r is r=z*z+p*p. I don’t understand this solution. My problem is: in a vector space with n dimensions there are n basis vectors. In the case of cylindrical...

If we want to show whether or not a specific Cosmic Ray particle is confined to our galaxy we must use the Larmor radius (relativistic version), r = γmc / qB Considering a 10^14 eV proton and assuming the galactic magnetic field strength is 10^−11 T, show that the particle is confined to the...

f(x) = 4x/(x-3)^2 Find the first five non-zero terms of power series representation centered at x = 0. Also find the radius of convergence.

I figured out that the focal distance is 19.01868

Hello! I am taking a course in nuclear physics using the book An Intro to the Physics of Nuclei & Particles by Dunlap. I am a little confused by an explanation related to the critical radius for nuclear reactions. The author first defines a value ##vq## as the average number of neutrons...

Homework Statement Calculate radius of rotating wheel. Linear speed of point "a" (red dot) is 2.5 times faster than linear speed of point "b"(blue dot) that is 5cm closer to center of wheel. Right answer is 8.33cm. I drew a sketch without linear line. Homework EquationsThe Attempt at a...

Why the height of liquid is not affected by the radius of U-Shaped tube . ..my textbook says this and it does make sense because if increase the radius of u shaped tube the height of liquid should decrease as the liquids take shape of their container. Edit : I could not make the title longer...

I have seen numerous sources for radii of atomic nuclii of various elements. One of the most common is the simple equation r=1.2 fm×A⅓, which makes sense if the nuclear density is constant for all elements and all isotopes. However, I've also found a table of measured nuclear charge radii that...

Homework Statement A cylinder rolls without slippage on a horizontal plane. The radius of the cylinder is equal to r. Find the radious of curvature of the trajectory of points A and B. Homework Equations Ciruclar motion equations. ##R=\frac{1}{C}## The Attempt at a Solution First I drew the...

I am studying how to determine the nuclear charge radius from direct measurement of the Coulomb energy differences of nuclei. My book says that there is strong evidence which suggests that the nuclear force does not distinguish between protons and neutrons. Thus changing a proton into a...

Homework Statement This is from a complex analysis course: Find radius of convergence of $$\sum_{}^{} (log(n+1) - log (n)) z^n$$ Homework Equations I usually use the root test or with the limit of ##\frac {a_{n+1}}{a_n}## The Attempt at a Solution My first reaction is that this sum looks...

Hi, I've computed 512 terms of a power series numerically. Below are the first 20 terms. $$ \begin{align*} w(z)&=0.182456 -0.00505418 z+0.323581 z^2-0.708205 z^3-0.861668 z^4+0.83326 z^5+0.994182 z^6 \\ &-1.18398 z^7-0.849919 z^8+2.58123 z^9-0.487307 z^{10}-7.57713 z^{11}+3.91376 z^{12}\\...

Homework Statement What is the potential at the center of the sphere relative to infinity? The sphere is dielectric with uniform - charge on the surface of the sphere. Homework Equations ##k=\frac {1}{4\pi\epsilon_0}## ##V=\frac {KQ}{r}## The Attempt at a Solution If the distance r=0 it would...

Homework Statement What is the ideal speed to take a 70 m radius curve banked at a 30.0° angle? Homework Equations tan θ = v2/r g The Attempt at a Solution This has me stuck, when I attempted this I came to the equation v= √ g*r* tan Θ But when I substitute in the variables, I enter then into...

(Apologies I posted this initially as a conversation. Not familiar with the format) I used the ‘gravitational time dilation’ equation to see how the clock rate varies with distance from the center of an object. I got the opposite result to what I was expecting.From Wikipedia; Gravitational...

1. Homework Statement A circle in a x-y coordinate system is given. The equation of the circle is unknown. The circle touches the x axes at (3,0). It also passes through the point B (0,10). Calculate the length of the circle radius? Homework Equations (x-p)^2 + (y-q)^2 = r^2 The Attempt at a...

Homework Statement A simple pendulum, suspended from a fixed point cosnits of a light cord of length 500mm and a bob of wieght 2N . The bob is made up to move in a hotizontal path. If the max tension is 4N show whether or not it is possible for the radius of the path of the bob to be 300mm...

So I've been able to solve A.12 inch B.24 inch C.75.3982 D.452.389 Cant solve e. Arc length can anyone please explain the formula. Thank you

I'm trying to build an oval bicycle wheel and need a formula to calculate the radii so that I can use the results to calculate the length for each spoke. See diagram for details. Hope someone can help.

I'm considering two identical spherical conductor each of radius ##a## and separated by a distance ##d##, and trying to figure out the capacitance of this configuration. My thoughts are that since capacitance is $$C=\frac {Q}{V}$$ and that the spherical conductors are equipotential surfaces...

Homework Statement Satellite orbits the Earth and its perigee r_min and tangential speed at perigee v_pe are given. The problem says do not use mass of Earth in the calculation, and use the only the constants g = 9.8 and radius of Earth 6380 km. I'm supposed to find the apogee and orbital...

Homework Statement What is the radius of the orbit of an electron traveling at 9.0 x 10^6 m/s around a zinc nucleus which contains 30 protons? Homework Equations I don't know if this problem can be solved quantum mechanically, all I can think of doing is solving it classically, using Coulomb's...

Homework Statement A stick of length 2L and of mass M spins with angular velocity ω around the axis perpendicular to the COM of the stick.It is rotating with making an angle Θ,with the axis parallel to Z axis.The COM has an initial velocity v=υ(to the y axis).Find it's precession radius R...

Hello, I'm given a problem of a mass rolling down an incline with mass 'm', radius 'r', and radius of gyration Rg, and I need to write the Lagrangian for the motion. I'm confused on why both r and Rg are given. Don't I just need one of the two for the moment of inertia? Thanks!

Can I calculate a tensor of a system( lots of particles) shaped like a sphere, then get exactly the radius of the system? (I want to get lengths of three axes of ellipsoid, and I'm trying to examine the way with a sphere. )

Homework Statement G= 6.67 *10^-11 M= 5.97*10^24 kg m= 430 kg Orbital speed=6800m/s I'm supposed to find radius of satellite orbit. Homework EquationsThe Attempt at a Solution I don't know where to start because in order to find radius, I have to find period as well

Homework Statement A yoyo falls straight down unwinding as it goes, assume has inner radius a, outer radius b and Inertia I. What is the generalised coordinates and the lagrangian equation of motion? Homework Equations L=T-U where T is kinetic energy and U is potential The Attempt at a...

If the radius unit vector is giving us some direction in spherical coordinates, why do we need the angle vectors or vice versa?

I try to get a correct result for the radius of a standard white dwark (roughly 10000 km). I just want the order of magnitude , i.e with the common values of a solar mass into Earth radius sphere. From http://www.astro.umontreal.ca/~bergeron/CoolingModels/Synthetic_Calibration.pdf page 1223...

Homework Statement Homework Equations V=kQ/R The Attempt at a Solution The answer is B)kQ/R. It is because V= k(2Q)/R. I don't understand why Q=2Q in this case. Isn't the point on the inside of the outer shell, so the Q for the equation is just Q?

I noticed that the Schwarzschild Radius Formula and the Escape Velocity Formula are actually identical. The Schwarzschild Radius is supposed to be one of the great equations generated from Relativity, while the Escape Velocity is something that was generated just using Newtonian gravity. All you...

Homework Statement A ball on the end of a string is whirled around in a horizontal circle of radius 0.250m. The plane of the circle is 1.06m above the ground. The string breaks and the ball lands 1.90m (horizontally) away from the point on the ground directly beneath the ball's location when...

Homework Statement A particle is moving clockwise in a circle of radius 2.50m at a given instant of time. I have to find radiant and tangential acceleration and the speed of the particle. The acceleration vector is 15.0 m/s² and the angle between the radius and the acceleration vector is 30°...

Homework Statement "Given a certain rocky material, estimate the greatest possible radius of a planet made up of said material" Homework Equations ##P = \frac{2}{3}\pi G\rho^2R^2## ##R = \frac{1}{\rho}\sqrt{\frac{3P}{2\pi G}}## The Attempt at a Solution I'm not quite sure of the validity of...

Would the velocity of a body which is orbiting another body change due to its radius to the center of gravity? If so, why? A body which moves passed a planet and starts orbiting it should have the same velocity it had before ,regarding the fact that it is orbiting a planet. Also, gravity isn’t...