Radius Definition and 1000 Threads

Homework Statement This is not so much an entire problem I need help with but just a part. It is a power series where after you do the ratio test, you end up with |4x^(2)| < 1, so |x^(2)| < 1/4. Since the radius of convergence is |x-a| < R, I end up with -1/4 < x^(2) < 1/4, but because...

There's something bothering me about the event horizons of black holes. The Schwarzschild radius (as I see it) is basically the distance from a center of mass at which the escape velocity is the speed of light. The way escape velocity is defined though is the speed a body must have to "reach...

Homework Statement a metal sphere of radius 0.39 m carries a charge 0.55 μC. Equipotential surfaces are to be drawn for 100-V intervals outside of the sphere. Determine the radius of the first, tenth and 100th equipotential from the surface. Homework Equations V = kQ / r Volt =...

Homework Statement What is the radius of gyration (in meters) for the steel flywheel shown? The width of its rim, L, is as given below. The density of steel is 7500 kg/m3. The outside diameter (OD)for the wheel is 2000 mm, and the inside diameter (ID) is 1840 mm as shown in the figure. The...

Homework Statement This is just a general question. When using Kepler's second law, which radius am I supposed to use to sub into r? Is it the radius of the object (ex. Earth's is 6.38e6 m) or the radius of orbit (ex. Earth's is 1.49e11 m)?Homework Equations C = (GM)/(4pi^2) = (r^3)/(T^2)The...

Homework Statement Find the Summation Notation and Radius of Convergence of this series. 5, x, 10, x, ... The Attempt at a Solution I don't know how did they come up with that equation.. But the summation seems right.. Can anyone tell me how did they arrive with that equation? I've tried...

Homework Statement I have a graph with the radius on the x-axis and Fc on the y axis. I had to then calculate the slope of this linear relationship. I did that, and I got 0.17. The problem is that I don't know what this represents. mass? acceleration?? Homework Equations Fc = m4π^2rf^2...

Physics puzzle: A 1" radius 7 billion K temp. ball is activated inside Jupiter... Physics puzzle: A 1" radius, 7 billion K temp. fireball is activated inside Jupiter...from an artificially induced fission reaction of .04kt. It is activated deep enough into Jupiter to be under 40,000,000...

Homework Statement Consider a simple model for the interior of the Earth: there is a spherical iron core with constant mass density ρ0 and radius a; outside the core is "rock" with constant density ρ1. Use these values for the densities: ρ0= 8.90×103 kg/m3 and ρ1= 3.80×103 kg/m3. The radius...

Is Schwarzschild radius trying to state the gravitational field on the event horizon of a black hole? If not, what is it trying to state? Can you give me a example using his formula to figure out the gravitational force of a black hole in the event horizon? Do you have any links I can...

I have a question, and I hope I can word it correctly. Say I have a round pipe of length 5 feet (actually, the length is irrelevant). I want to bend it at a certain radius in the horizontal direction, and also a certain radius in the vertical direction. Let's say I bend it at 20' horizontal...

Homework Statement A satellite is in orbit just above the surface of a spherical planet which has the same radius as Earth and the same acceleration of free fall at it's surface. Calculate: i) Speed ii) Time for 1 complete orbit. Radius of Earth = 6400km or 6400000m and accel. of free...

can anyone say why the derivation works? my teacher went through it in class and sort of said "don't question it" (which i hate) but it's still annoying me now even though it's a few weeks since i finished college. KE = GPE 0.5mv² = GMm/r r=2GM/v² and then if the escape velocity is the...

I have problem to see clearly the case of rotation of a body about a point with decreasing radius.this can be viewed as a body being rotated about a point with the help of a thread which passes through a hole in a disc and the thread is being pulled to apply a tension and gradually to decrease...

Homework Statement The radius r of a wire of length L increases according to r = a * exp(bx^2), x is the distance from one end to the other end of the wire. What is the resistance of the wire?Homework Equations R =\frac{L * \rho}{A}The Attempt at a Solution dR =\frac{dx * \rho}{A} A(r) = \pi *...

Im new to these forums and I'm looking forward to becoming a regular contributor. I'm attempting to prepare for physics in the fall and I have a textbook problem that i understand the process of solving but not understand the concept. Heres the question: What mass of a material w/ density p...

Are there any known metrics in which black holes do not have the Schwarzschild radius? Specifically, I'm interested in whether it's possible for a black hole to have an event horizon which is not of the form: constant * mass.

Frictionless, horizontal table...radius and speed...? The 0.20 kg puck on a frictionless, horizontal table is connected by a string through a hole in the table to a hanging 1.20 kg block. With what speed must the puck rotate in a cicle of radius 0.50 m if the block is to remain hanging at rest?

Does anyone know how to determine the leading-edge radius of an airfoil using just the x y coordinates.

A cart slides down a frictionless inclined track to a circular loop of radius R = 13 m. In order for the cart to negotiate the loop safely, the normal force acting on the cart at the top of the loop, due to the track, must be at least equal to the cart's weight. (Note: This is different from the...

In the Schwarzschild spacetime setting we have a vacuum solution of the Einstein field equations, that is an idealized universe without any matter at the geodesics that are solutions of the equations. This spacetime has however a curvature in both the temporal and spatial component that comes...

How do I go about finding the radius of the circle, I seem to be stumped on this question? *dimensions in attachment are not to scale, just a rough sketch.

I understand that the holographic principle applies to black holes and states that they are objects of maximum information/entropy. It states further that this information/entropy is bounded by the black hole's area rather than its volume. Apparently the holographic principle might apply to...

Homework Statement Determine the polar moment of inertia and the polar radius of gyration of the shaded area shown with respect to point P. http://imgur.com/8Kc1S Homework Equations Jp = Ix + Iy Ix = &int y^2dA Iy = &int X^2dA The Attempt at a Solution A = 2(a/2)(a) +...

Homework Statement Find a differential equation whose solution is a family of circles with centers in the xy-plane and of variable radii. Hint: Write the equation of the family as x^2+y^2-2ax-2by+2c=0 Homework Equations The previous questions asks to find a differential equation whose...

Homework Statement I need to calculate the radius of curvature of a bimetallic strip when the two strips are subjected to different temperatures. in the problem, the two metals themselves are in different temperatures. One at 180°C, other at 160°C. Anyone with good solid mechanics knowledge...

I am on my second year of study for a bachelor of medical and radiation physics and one of my friends who is studying mechanical engineering ran this question by me, I haven't really had time to go into it in any detail, i thought some of you guys might like to give it a crack: You set out to...

Hi all, these questions have nagged me for years and I have never found a text or a paper that even addresses them. Regarding photon "radius", what is the maximum width that two slits can be spaced which still permits the double-slit phenomenon to occur? Would this be a valid method of...

An object is accelerated close to c. Does the relativistic mass contribute to the sch. radius as seen by an observer? Is it simultaneously a black hole and not a black hole?

I am trying to figure out the minimum radius needed to avoid voltage breakdown. I found this from a Physics website: "The electric field near a conductor is inversely proportional to the radius of curvature of the surface." So if I know the voltage and the distance between the 2 metal...

there' s a problem that tells " estimate the radius of a planet that a man can escape it's gravitation only by leaping vertically upward..that density of the planet is assumed to be same as earth..." it seems to me that there's not enough information provided here to solve the problem...

Homework Statement I'm trying to figure out the radius of a circle that intersects two points on a right triangle. One side of the triangle is tangent to the circle and the other intersects it. I have attached an image that helps further explain what I'm talking about. Knowing what I have...

I'm trying to figure out the radius of a circle that intersects two points on a right triangle. One side of the triangle is tangent to the circle and the other intersects it. I have attached an image that helps further explain what I'm talking about. Knowing what I have listed in the image is...

Homework Statement An aircraft remains in flight by generating a force, called Lift, which acts to counter gravity. By design, Lift always acts in the “up” direction of the aircraft frame of reference (i.e., orthogonally to a lateral axis along the wings). An aircraft turns by banking its...

I have that \left( \frac{dR}{d \tau} \right)^2 = ( 1 - \epsilon)^2 ( \frac{R_{\text{max}}}{R}-1) describes the radius of the surface of a collapsing star in Schwarzschild geometry. I need to show it falls to R=0 in time \tau = \frac{\pi M}{(1-\epsilon)^{3/2}} So far I have rearranged to get...

Does centripetal acceleration increase with a greater radius? According to a = v^2/R, it does not. According to a = (omega)^2R, it does. So which is it? I think that as you go further out to a greater radius, speed also increases, and so a = v^2/R would also make sense in terms of a greater...

Homework Statement sum ((x-1)^(2n-2))/((2n-1)!) n=1..infinity? after doing the ratio test, i found that the radius is from negative infinity to infinity (converges for all x). is this right? if not can you steer me in the right direction, please. Homework Equations The Attempt...

a disc of radius r we have to find electric flux at a point which is at a distance r from the centre i have used e=(sigma/2eo)(1-x/sqrt(r^2+x^2)) the area da=2pir*dr i know flux=closed integral (e.da) and x=r after that what should i do Reply With Quote

Homework Statement Homework Equations i guess its r=sqrt(I/A) where A is the area of the circle thing and I is the moment of intertia. The Attempt at a Solution I guess I'm just having trouble getting I. A is 33pi

The problem: "A convex spherical mirror is 25 ft from the door of a convenience store. The clerk needs to see a 6 ft. person entering the store at least 3 inches tall in the mirror to identify them. What is the radius of the mirror?" d_obj = do = 25 ft = 300 inches h_img = hi = 3 inches...

Homework Statement How would I find the radius of convergence of this series? f(x)=10/(1-3x)2 is represented as a power series f(x)=\sum from n=0 to \infty CnXn Homework Equations The Attempt at a Solution Okay so I tried deriving, using d/dx(1/1-3x)=3/(1-3x)2 and ended up with...

Homework Statement If Dr is a closed disk of radius r centered at (a,b) find lim r->0 (1/pir2) \int\intfdA over Dr. The Attempt at a Solution From mean value equality, \int\int fdA = f(x,y)A(D) where A(D) is the area of the region which here is pir2. So the lhs becomes lim r->0 f(x,y)...

Homework Statement This is the question of mine that I'm having a little confusion about. I know the whole process in which you use the ratio test to determine the radius of convergence and using that you test the end points of the summation to see if they converge at the end points aswell...

Hi, Does the following inequality hold regarding the product of 2 matrices A and B: p(AB) <= p(A)p(B), where p denotes the spectral radius. Thanks!

Homework Statement Determine the radius of convergence, the interval of convergence, and the sum of the series Summation from k=2 to ∞ of k(x-2)^k+1. Homework Equations ratio test? The Attempt at a Solution possibly take the derrivitive of the power series, then find the sum then integrate...

Homework Statement \Sigma (from index k = 1 until infinity) Within the Sigma is the series : (k! * (x^k)) Homework Equations Ratio Test : lim as k approaches infinity |a(k+1) / ak| The Attempt at a Solution When I apply the ration test to the series and simplify I get lim k...

Greetings everyone and thanks in advance for any help you can offer. I am currently part of a team tasked with designing and constructing an autonomous, mechanically powered two-axle vehicle capable of making left-hand u-turns around a set track. I have designed a steering mechanism I...

Hello everyone! I'm trying to find out how to precisely construct three congruent circles inside a larger circle, each tangential to both the outer circle and the other two circles. For example: http://img4.imageshack.us/img4/1044/verybasicdrawing.png An image I found on the internet...

A method to get the Laurent series of a complex function is by undetermined coefficient.For example f(z)=cot(z)=cos(z)/sin(z).If we want to get the Laurent series of cot(z),we can expand cos(z) and sin(z) to Taylor series respect,then assume the series of cot(z) is a_{ - 1} z^{ - 1} + a_0 z^0...

Homework Statement There wasn't a figure given. All that was given was that the figure is a circular ring. Theta is the angle between the electric field direction and a unit vector normal to the surface area of the ring. Flux versus costheta was plotted and a slope was found to be m = 0.172. E...