Radius Definition and 1000 Threads

Homework Statement To assemble a uniformly charged sphere, assemble it like a snowball, layer by layer, each time bringing in an infinitesimal charge dq from far away and smearing it uniformly over the surface, thereby increasing the radius. How much work dW does it take to build up the radius...

Homework Statement Find the hill radius of Earth and calculate the velocity of an object falling from that radius (and from rest from the Earth's frame) at the point where it impacts the Earth. Relate this velocity to the escape velocity of Earth. Homework Equations Hill radius: r_h=R...

How can SSM be utilized to predict the radius of the Sun when it becomes a red giant?

Hello, First off, I'm not a physics student by any means, but it does intrigue me. I've been wondering about the Schwarzschild radius, and how the density of an object dictates the escape speed. Why is it, that the more you compress an object, the more gravity it "owns?" If you were able to...

Homework Statement A 135 kg satellite experiences a gravitational force by the Earth of 960 N. What is the radius of the satellite's orbit. And altitude? I already found the radius and I came up with 7489.99 km. I just need help finding the altitude. Homework Equations Equation for...

I am interested in knowing if the inside radius of the inner most part of the electron cloud is a constant versus Z. For example is it always the Bohr radius, or does this inner radius change as a function of Z? What is the experimental evidence?

Homework Statement Consider a hollow cylinder of radius 10 m., length 50 m., and charge 6 C., and a rod with radius 4 m., length 50 m., and charge -4 C. The rod is uniformly placed inside the center of the hollow cylinder. What is the electric field at radius = 15 m.?Homework Equations...

Hi! I am extremely confused on what seems to be quite a simple question. The question contains a graph of root mean square radius <r^{2}> plotted against A^{1/3} where A is the nucleon number. In the lecture notes he specifies that <r^{2}> is not the same as R but does not really say...

I've been trolling for this answer on the Internet but can't find a simple explanation. If I have two airplanes of different mass, both flying at the same speed, which plane has the larger turning radius and why? It seems like the more massive plane would require the larger turning radius due...

Does anyone have an intuitive explanation for why torque depends on the perpendicular distance from the axis of rotation? I understand the maths and fully accept the truth of the description, but CANNOT wrap my brain around the reason. The ball and spring model of a solid seems like a place to...

So I was reading a thread on PF talking about the radius of a solenoid and Bob S answered with a link: On that site, it states that the Radius = the outer radius - the inner. It doesn't make sense. What happens when there is only one layer of coil and the outer radius (OR) is basically the...

The Schwarzschild equation for a black hole's event horizon is rsh = 2GM/c2 or (1.48 x 10-27 m/kg) x M. Thus, the ratio of mass to radius is 6.7 x 1026 kg/m for all black holes. If the mass and radius of the universe are calculated as follows, Mass of the gravitationally connected universe...

Homework Statement I have to turn this homework in online... I just want someone to check my work Convert from Cartesian coordinates to Polar coordinates (-1,-sqrt(3)) if r > 0 and if r < 0. Homework Equations The Attempt at a Solution if r > 0 then I believe the answer is...

Hi, I want to calculate a volume integral of a function f(r,theta). The limits for azimuthal and polar angle is of course 0-2*pi and 0-pi, respectively. But the limits for the radius is 0 to an expression depending on the polar angle. Can I simply first integrate the r-part, say from r^4 to...

What is the radius of curvature formula for an ellipse at slope = 1? I have found b^2/a, and a^2/b for the major and minor axis, but nothing for slope = 1. Thanks.

Hi guys, I've been struggling with this concept for a few days now. I have this *good* image that I am blurring (using a gaussian blur), then adding some small percentage of gaussian white noise to it. Then from that image, I want to compute the naive solution (just assuming B=AX and solving...

Homework Statement If the radius of theCD below is 6.0cm and the angular velocity is 5.0 rad/s , what's is its angular displacement in 2.0s ? Homework Equations Delta θ = ωt+.5∂t^2 The Attempt at a Solution I know the angular velocity and the time but how can I find out the radial...

x^n/(2n-1) is the series. It starts at 1 and goes to infinity. I did the ratio test on it and got abs.(x) So the radius of convergence=1, and then I plugged -1 and 1 into the original series and got that they both converged. But the answer is [-1,1). Why aren't they both hard brackets?

Homework Statement A spherical rain drop carries a charge of 5×10-6 C and has a potential of 8.800×10-8 V at the surface. Find the radius of the drop. Homework Equations V = (kQ)/r The Attempt at a Solution I simply moved V and r to their respective spots and plugged in my...

When I watch the spacetime diagram of a particle inside the Scharzshield radius, it seems that the particle can move 'horizontal' (they move dr while X0 stays constant). Does this mean the particle can move faster than light inside the Schwarzschield sphere? Or does the meaning of space/time...

How can I describe mathematically that if you take some mass m with some density d as the radius tends to 0 the density tends to \infty I'm not exactly sure what it is I'm trying to describe I'm just looking for something that describes when the radius of an object decreases, the density...

Hello, would someone know what is the smallest radius of curvature achievable with current gradient index optics (GRIN) technology? I mean, how much could one "curve" a ray of light? Many thanks! :smile:

The cosmological "Big Rip" and a shrinking Hubble radius Doesn't an expanding universe forecast such outcomes as a faded and unobservable cmb, galaxies moving away from each other greater than the speed of light, a gravitationally unbound solar system, and eventually an observable universe...

An effort to understand the physical implications of the Hubble radius. I start by assuming a flat radial FRW metric given by: ds^2 = - c^2 dt^2 + a(t)^2 dr^2 Let us assume that we are holding one end of a rigid ruler with the other end out in space at a fixed proper distance R away from us...

Does anyone have a reference for experimental and/or estimated Van der Waals radius for the molecule hydrogen deuteride ? Symbolically, this would be a proton {(p)e-} + {(np)e-} deuterium. I would like to know how closely the two atoms can approach each other to maintain the stable state of a...

1. A 55 kg airplane pilot pulls out of a dive by following, at constant speed, the arc of a circle whose radius is 320 m. At the bottom of the circle, where her speed is 230 km/h, what is the magnitude of her acceleration? Homework Equations v^2= vi^2 +2a(x-xi) The Attempt at a...

A hexagon with consecutive sides of lengths 2, 2, 7, 7, 11 and 11 is inscribed in a circle. Find the radius of the circle.

The Schwarzschild Radius of an object is the length such that if the object is shrunk down that small, the escape velocity becomes equal to the speed of light. That being said, however, the escape velocity of any gravitational body matters where it is measured relative to the center of mass...

What is the radius of a photon's circular orbit around a mass M? My guess would be the Scharzschild radius. Is that true?

Hi all, I have found this formula being used but I am not sure what it means. It is used to find the radius of a circle in a sector. Hope you can help me understand it. sin(π/6) = r/(6-r) r is the radius of the circle itself and 6 is the radius of the sector or the circle of the sector...

When the radius of the circle decrease the object moves faster(With the same force) I believe this is a misconception .In common sense the object revolves around more,This leads us to think that it is moving fast but actually the object moves the same distance.Am I right?

Homework Statement Suppose that r = f (θ) defines a polar graph. Find an expression for dx/dθ. It should not involve the letter r. Explain a procedure to determine the farthest that the graph r = f (θ) extends to the left and to the right (Hint: If x = x0 is the x - value of the point that...

Let us consider the case of a body falling down radially towards a Schwarzschild black hole. The velocity of the body is as high as it would be if it had been falling from standstill at infinity. When the body finally fuses with the black hole (get infinitely close to the Schwarzshild...

A=\pir^{2} therfore, \frac{dA}{dt}=2\pi\frac{dr}{dt} The question is if \frac{dr}{dt} is constant is \frac{dA}{dt} constant? To me, I know that if the change in radius with respect to time is constant, The rate of change of the are with respect to time still depends on the radius of...

Homework Statement I need to develop a macroscopic gravity simulation software. I have problems with representing vectors in a programming language (c++), because I need do develop my own mathematical infrastructure for the project. I asked for the Cartesian coordinates, but would also have...

Homework Statement Ʃ(((-1)^n)(x^n))/(n+1) from 0 to ∞Homework Equations The Attempt at a Solution I took applied the ratio test and got that lim|(x^(n+1))/(n+2) * (n+1)/(x^n)| =|x| so that means for it to converge |x|<1 Radius of convergence is 1 My interval is (-1<x<1) Now I check the...

What is the radius of the de broglie circular orbit with n=1?

Homework Statement The coefficients of the power series \sum_{n=0}^{∞}a_{n}(x-2)^{n} satisfy a_{0} = 5 and a_{n} = (\frac{2n+1}{3n-1})a_{n-1} for all n ≥ 1 . The radius of convergence of the series is: (a) 0 (b) \frac{2}{3} (c) \frac{3}{2} (d) 2 (e) infinite Homework EquationsThe Attempt at...

Imagine that we have a wheel spinning with the axis of rotation normal to the Earth's surface. For convenience, let's assume that the wheel is located somewhere in the north hemisphere. According to the definition of the Coriolis force, every little particle dm of the wheel has a coriolis...

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...

How to derive "dark energy" density from Jorrie's Hubble radius limit (c^4/(8 pi G))*3*(17.3e9 light years)^(-2) Paste that in the google window, and see what you get. When I paste that into google I get 0.5393 nanopascal, which is equivalent to 0.5393 nanojoule per cubic meter. If 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.

Homework Statement An Aluminum cable of length 3.5m has 15,000 N tensile force acting on it if the wire is only allowed to be stretched by 1mm before it breaks, What must be the radius of the wire if the Young's modulus of Al is 6.9 x 10^10 N/m^2? I am also supposed to find the tensile...

Huygens' belief was that every wave is made up of smaller wavelets, which are basically circles. I was wondering, is the radius of these wavelets equal to the length of the wavelength of its wave? I have another related question: If a wave is passing through a slit, what is the maximum...

Points A, B, C, D are on a circle with radius R. $$|AC| = |AB| = 500$$, while the ratio between $$|DC|$$, $$|DA|$$, $$|DB|$$ is 1, 5, 7. Find R.

Homework Statement A Copper wire has a shape given by a radius that increases as R(x)= aex+ b. Its initial radius is .45 mm and final radius is 9.67 mm and its horizontal length is 38 cm. Find its resistance. Homework Equations R = pL/A where p = resistivity of copper A = ∏r2 L = length of...

Homework Statement A 100g (0.1kg) rock is attatched to a 1.0m rope and spun around in a circle with a period of rotation of 1.0s. What is the Radius of the circle that it forms? Homework Equations Fc = (mV^2) / r V= (2∏r/T) LCosθ = r The Attempt at a Solution Im quite stick...

Thanks again to those who participated in last week's POTW! Here's this week's problem! ----- Problem: A point is uniformly distributed within the disk of radius 1. That is, its density is\[f(x,y)=C,\qquad 0\leq x^2+y^2\leq 1\] Find the probability that its distance from the origin is less...

Homework Statement Two remote planets consist of identical material, but one has a radius twice as large as the other. IF the shortest possible period for a low altitude satellite orbiting the smaller planet is 40 minutes, what is the shortest possible period for a similar low altitude...

The centers of three circles are situated on a line. The center of the fourth circle is situated at given distance d from that line. What is the radius of the fourth circle if we know that each circle is tangent to other three. Please give me a hint, if you can. Answer: $$d/2.$$