Radius Definition and 1000 Threads

The most widely cited figures are 1.4 solar masses and 10 km radius. However, tracing the references back to their sources I find that these are just canonical numbers for a generic neutron star. Either the original paper says that explicitly or says something like, "Let's assume a mass of...

Maybe I'm plugging my website but I just finished writing a versatile cylinder calculator. If you know two variables (Volume Area Radius Height), it calculates the other two. http://www.1728.org/diam.htm It was a little tricky deriving the formulas but I'm glad I did. (Yes, I know if you...

What if Schwatzchild has made the same mistake as Newton? ( 1 - 2MG / c2 r ) dt can be view as a binomial expansion to first order of 1 / ( 1 + 4MG / C2 r )1/2 dt then would the event horizon be at the singularity? I've been reviewing Susskind's online lecture series, and...

Homework Statement A lens of power of -5.0D has a surface which is convex of radius of curvature of 15.0cm. The lens is made of material of refractive index of 1.50. What's the radius of the other surface of lens? Homework Equations The Attempt at a Solution since power = 1/f...

Homework Statement by taking the lower curvature as r1 , and the upper curvature as r2 , i don't know whether r1 is 20cm , r2 is 10cm or vice versa. But according to the ans r1= 10 cm , r2= 20cm . why is it so? Homework Equations The Attempt at a Solution

Homework Statement when the glass is partially cut( as shown in the photo ) , the centre of curvature is inside the denser medium (glass), so the centre of curvature should be lower than point Q in the diagram . am i correct? by saying that the centre of curvature is inside the denser medium...

Homework Statement Show that if given \mathbf{x}_0, and a matrix R with spectral radius \rho(R)\geq 1, there exist iterations of the form, \mathbf{x}_{n+1}=R\mathbf{x}_0+\mathbf{c} which do not converge. The Attempt at a Solution Let \mathbf{x}_0 be given, and let...

Can someone show me how to resolve this question? A particular circle in the standard (x,y) coordinate plane has an equation of (x − 5)2 + y2 = 38. What are the radius of the circle, in coordinate units, and the coordinates of the center of the circle? radius center F. √38 ( 5,0) G. 19 ( 5,0)...

I was thinking a bit earlier: What if you created a particle at infinity (ignore the normal particle rules for simplicity), and allowed it to fall towards a massive body? Ignoring other effects such as the other forces, would the particle ever gain enough energy to surpass the energy...

Homework Statement If the acceleartingb voltage remains constant, but the current through the hemholtz cois is increased, what would be the effect on the radius of the circular motion of the electrons? Homework Equations The Attempt at a Solution

Homework Statement An electron with speed v, undergoing cyclotron motion in a transverse magnetic field B(r) at cyclotron radius r0, given r0 = mv/[eB(r0)], can be accelerated by ramping the B field in time. (a) Since magnetic fields do no work,what is increasing thwe kinetic energy of the...

find the taylor series for $f(x)=x^4-3x^2+1$ centered at $a=1$. assume that f has a power series expansion. also find the associated radius of convergence. i found the taylor series. its $-1-2(x-1)+3(x-1)^2+4(x-1)3+(x-1)^4$ but how do i find the radius of convergence?

Hi, how do I find the center and radius from these equations? The 2 equations represent 2 different circles, by the way. I need to draw 2 circles.

Hi, how do I find the center and radius from these equations? The 2 equations represent 2 different circles, by the way.

Homework Statement It is given that the period of Mercury is 87.9 days and the angular speed of Mercury is 8.27*10^-7 I am asked to find the radius of Mercury. I have no idea how to calculate the radius just the two pieces of information given. Should there also be the linear velocity of...

Hello. How do I find the radius of convergence for this problem? ##\alpha## is a real number that is not 0. $$f(z)=1+\sum_{n=1}^{\infty}\alpha(\alpha-1)...(\alpha-n+1)\frac{z^n}{n!}$$ I understand that we can use the ratio test to find R. And by using ratio test, I got R=1. But in the...

Hello. How do I find the radius of convergence for this problem? $\alpha$ is a real number that is not 0. $$f(z)=1+\sum_{n=1}^{\infty}\alpha(\alpha-1)...(\alpha-n+1)\frac{z^n}{n!}$$

Homework Statement The uniform 45.6 mT magnetic field in the picture below points in the positive z-direction. An electron enters the region of magnetic field with a speed of 5.29E+6 m/s and at an angle of θ = 30.1° above the xy-plane. Find the radius r and the pitch p of the electron's spiral...

Hello. I am stuck on this question. I'd appreciate if anyone could help me on how to do this. The question: Expand the following into maclaurin series and find its radius of convergence. $$\frac{2-z}{(1-z)^2}$$ I know that we can use geometric series as geometric series is generally...

Hello. I need explanation on why the answer for this problem is R = ∞. Here's the question and the solution. Expand the function into maclaurin series and find the radius of convergence. $zsin(z^2)$ Solution: $$zsin(z^2)=z\sum_{n=0}^{\infty}(-1)^n\frac{z^{2(2n+1)}}{(2n+1)!}$$...

Hello. I need explanation on why the answer for this problem is $R=\infty$. Here's the question and the solution. Expand the function into maclaurin series and find the radius of convergence. $zsin(z^2)$ Solution: $$zsin(z^2)=z\sum_{n=0}^{\infty}(-1)^n\frac{z^{2(2n+1)}}{(2n+1)!}$$ Divide...

hi guys, I have been doing a research on white dwarf stars and chanrashekhar limit. I need to plot a graph for the mass-radius relationship of the dwarfs. from the equalization of the hydrostatic equilibrium pressure and the electron degeneracy pressure I found out the radius -mass relationship...

Homework Statement hi all, why the wave is reflected back form the centre when it is at the distance of 200mm? why the wave can't go beyond 200mm to reach 250mm from the side of bowl? Homework Equations The Attempt at a Solution

Find the radius of the circular section of the sphere of the sphere x^2 + y^2 + z^2 = 49 by the plane 2x+3y-z-5 \sqrt{14}= 0

T (Gy) R (Gly) 0.00037338 0.00062840 0.00249614 0.00395626 0.01530893 0.02347787 0.09015807 0.13632116 0.52234170 0.78510382 2.97769059 4.37361531 13.78720586 14.39993199 32.88494318 17.18490043 47.72506282 17.29112724 62.59805320...

I am trying to compute the geodesic (or tangent) radius of curvature of the geodesic circle by using the below formula. \frac{1}{\rho_c}=\frac{\partial G/\partial S}{2\sqrt{E} G} where s is the arc length parameter and E, G are the coefficents of the first fundamental form. Can you...

[b]1. A bug walking on a circular flowerpot completes one lap around the plantar in 12.86s. If the radius is of the plantar is 11 cm, how fast was it traveling? Answer in cm/s. [b]2. Homework Equations [b]3. The Attempt at a Solution I tried dividing the diameter of the...

We've just started learning about ψ in the quantum mechanics section of our atomic structure chapter. So while reading, I found these graphs where they used certain units along the y-axis for the graphs for ψ and radius (in nm), and ψ^2 and radius. What units are these exactly? My chemistry...

Rolling sphere, problems with the fundementals. Homework Statement A sphere with the mass of 2.5 kg rolls without slipping. The speed of the center of gravity is 10 m/s. a) Calculate the translational kinetic energy of the sphere b) Calculate the rotational energy of the sphere c)...

Homework Statement Pic: http://i.imgur.com/Ny4YAKf.jpg Rod has radius R, and mass M. Small mass has mass m. I have to find gravitational force exerted on mass m by rod and potential energy of the whole thing. Homework Equations The Attempt at a Solution So my idea is that...

If you have an object that undergoes a free fall from on a planet Mars which experiences a gravitational acceleration of magnitude 3,8m/s(squared) the mass of mass is given to be 6,4*10^i23kg. Please how do I find the radius of mars

Homework Statement A closed cylinder is required to have a volume of 40m^3 but made with the minimum amount of material. Determine the radius and height the cylinder must have to meet such a requirement. V= πr^2h Steps needed: a) Insert value and transpose for h b) Then sub into...

Homework Statement Homework Equations r=mv/qb mv=sqrt(2*KE*m(alpha)) m(alpha)=6.64e-27 kg The Attempt at a Solution i was just wondering how to get the answer (7.6e-4 m). i get path curving down, and do r=sqrt(2*1e3eV*6.64e-27kg*1.6e-19J/eV)/(q*B) =15.18e-4m so to get the...

Please help me with this astronomy problem. I am supposed to calculate the smallest planet that is detectable with the transit method, given a signal to noise ratio and a star's radius: Suppose the star is seen at its distance D with a signal to noise ratio of S/N = 10^4. This means that in...

Homework Statement GMR_{hollow cylinder}=Re^{-Kμ} where K=\frac{AR^4-R^2r^2+Br^4+r^4ln(R/r)}{(R^2-r^2)^2}, where R is the outer radius and r is the inner radius, and mu is the relative permeability. We are to determine the numerical values of A and B. I am stumped on how to begin attempting...

Okay, so the job I need to do is derive an equation for the radius of an object in terms of its frequency. These are the equations that we are allowed to use: v(Linear velocity) = rω v=2πr/T ω (angular velocity)=2πf f (frequency)= 1/T (time period) T= 2πr/v a (centripetal...

Homework Statement determine the radius of convergence of the series expansion of log(a + x) around x = 0 Homework Equations The Attempt at a Solution So after applying the Taylor series expansion about x=0 we get log(a) + SUM[(-1)^n x^n/(n a^n)] I understand how to get the...

Homework Statement I've found that the typical way for using ratio test is to find the limit of an+1/an However, my tutor said that radius of convergence can be found by finding the limit of an/an+1 and the x term is excluded. For example:Finding the interval of convergence of n!xn/nn my...

Homework Statement Some kid is playing with a yoyo of mass m. The yoyo string is let out to length L, and is spun in a horizontal circle at a constant rate of ω. The yoyo string makes an angle of θ with the horizontal m = 39 grams = 0.039 kilgrams L = 46cm = 0.46m ω = 3 rads/sec...

Given Cartesian (x,y,z), Spherical (r,\theta,\phi) and parabolic (\varepsilon , \eta , \phi ), where \varepsilon = r + z = r(1 + \cos(\theta)) \\\eta = r - z = r(1 - \cos( \theta ) ) \\ \phi = \phi why is it obvious, looking at the pictures (Is my picture right or is it...

Suppose we have a planet of mass m orbiting a larger one of mass M along an elliptical path. If we use polar coordinates with the origin placed on the planet of mass M (focus of the ellipse) then at the instant when the smaller planet is at the point of closest approach we have: \boldsymbol{v}...

Hello, this isn't a homework problem, so I'm hoping it's okay to post here. I would like to know the correct way to mathematically express the idea in my title. It is intuitively obvious that as the radius of a circle increases, it's curvature decreases. I looked it up and found that...

Relating to the synchronous nature of the moon’s rotation and orbit around the earth, what would happen if the orbital radius of the moon were slightly increased? I want to ignore tidal locking or gravitational gradient, and just look at it from an angular momentum perspective. Would...

The problem is stated in the attachment. I would include my attempt at the question if I got anywhere. I'm really only looking for a hint as to how I set up the solution. PS, I understand how to work out the angle if the car wasn't moving. Thanks Homework Statement...

Homework Statement If you lived on a planet with five times the mass of Earth and twice the radius, what would be the gravitational acceleration at the surface of your planet? Homework Equations GM/r^2 Mass of Earth = 6.00*10^24 kg Radius of Earth = 6.38*10^3 km The Attempt at a...

When being burned in a writable CD-R Drive, the angular speed is often faster when playing audio... When writing along the outer edge, the angular speed of one drive is about 4800 RPM (Revolutions per minute). Find the linear speed. The question above it, or before this one was with CD's radius...

A magnetic field of 0.0200 T (up) is created in a region a)find initial magnetic force on an electron initially moving at 5.00x10^6 m/s (N) in the field b) what is the radius of the circular path Equations used: a) F=qvB b) F= kq/r^2 Thanks in advance

Homework Statement A computer scientist has dropped a tiny pizza crumb onto a magnetic disk. Later, when it's turned on, the disk is rotating at 88 revolutions per second about its axis, which is vertical. The coefficients of kinetic and static friction between pizza crumbs and the disk are...

Homework Statement here's the question, is my concept correct? the ans is 9.86 cm, but my ans is 13 cm, can anyone tell me which part is wrong? Homework Equations The Attempt at a Solution