Radius Definition and 1000 Threads

Homework Statement My professor mentioned something called "areal radius" briefly in class, but it's I'm unclear as to what it means. It doesn't appear in the index of any textbook I have, and google is pretty unhelpful since it parses it as "area" or "a real" and returns lots of results like...

Homework Statement A carnival ride has a large horizontal steel disc of radius 5.0 m from which cars are suspended by 6.0 m long chains. The disc is rotated about its axis so that the cars swing out and revolve in a circular path. At its operating speed, the angle of the chains to the...

Homework Statement A disc shaped object is made of a non-uniform material. Its radius is r and it is fre to rotate about an axis through its centre. If a force F applied tangentially at the edge of the object produces the angular acceleration a, what is its moment of inertia for rotation...

Homework Statement We are given the mass of the sun, ms = 1.99 x 10^30 and the mass of the venus, mv = 4.83 x 10^24. The distance from each other radius is r = 1.08 x 10^8. What is the centripetal acceleration? mv = 4.83 x 10^24 kg ms = 1.99 x 10^30 kg r = 1.08 x 10^8 km G= 6 67x10^-11 N m2...

A circle has Centre 0 and radius 2. A, B and C are points on the circumference of a circle such that AB is the perpindicular bisector of 0C. Find the area of the segment of the circle bounded by the line segment AB and the minor arc ACB. Give the area in exact forms in terms of surds and...

Homework Statement \sum from n=1 to inf (1+ 1/2 + ... 1/n)x^n Find the radius of convergence and the interval of convergence of the given power series. Homework Equations Dunno.. The Attempt at a Solution Stuck thinking about it. I'm not sure if I can combine what's in brackets with the...

Homework Statement I think I've just majorly confused myself here... In the above diagram, since the ball doesn't "slip" we know that R*\frac{d\theta}{dt} = V where theta is the angle of rotation on the disk itself. I need to relate the angle phi to the angle theta. If I use...

How do you derive the average abs(y) value of points on the surface of a sphere with a radius of 1 centered at (x,y,z)=(0,0,0)? I'm assuming that the points are sampled evenly, or that you can integrate for all points without any distortions that result by averaging over the xy-plane. How do...

Creating metallic hydrogen has proved more difficult than expected. One explanation would be that the Bohr radius of Hydrogen is smaller than expected. Is there any other evidence of an error in Bohr radius predictions?

Homework Statement Our teacher was talking about something regarding two tangent lines on a circle who distance between the tangent lines is square root of 3 times the radius of the circle... She wanted us to find the proof of this but I am stumped on where to even look... Does anyone know...

:cool:Hi all, I've been trying to solve the attached question for a long time, but it didn't help. I don't know how to start solving it. Could someone help me please :( Thnx Ted

Electron orbiting proton--orbital radius?? Homework Statement In the Bohr model, the electron is imagined to move in a circular orbit about a stationary proton. If the speed of the electron were 8.9e5 m/s, what would be the corresponding orbital radius? 2. Homework Equations 3...

The Problem: Why is it that r = rrE + h? r = distance from Earth's centre to satellite rrE = Earth's radius h = altitude Why is it that you find altitude by subtracting Earth's radius from radius? How does that make sense..

Homework Statement In the Bohr model, the electron is imagined to move in a circular orbit about a stationary proton. If the speed of the electron were 8.9e5 m/s, what would be the corresponding orbital radius? Homework Equations The Attempt at a SolutionFe=ma Fe=ma a=Fe/m (v^2)/r=(kqq/r)/m...

Homework Statement Suppose the coefficient of static friction between the road and the tires on a car is 0.789 and the car has no negative lift. What speed will put the car on the verge of sliding as it rounds a level curve of 39.3 m radius? Homework Equations i know the equation for...

Homework Statement If a pipe is between two blocks... one block being 1 inch tall and the other block being 2 inches tall. Between the two blocks is an arc that is 6 inches... What is the radius? Can some one please help me... I have no Idea what to do.. thank you.

Hello, we been set a physics assignment where we are given a table of data, a spaceship approaches a planet, and the velocity and radius are given at certain points, we have to graph velocity against 1/r and hence find the mass of the planet. I really don't get this question, i tried slope...

The question: A particle in a cyclotron gaines energy q \Delta V from the alternating power supply each time it passes from one dee to the other. The time interval for each full orbit is T = \frac{2 \pi}{\omega} = \frac{2 \pi m}{q B} so the particle's average rate of increase in...

Homework Statement Given the potential energy V(r)=-\frac{1}{4\pi \epsilon_0}\frac{e^2}{r} (where e is the unit charge), use the uncertainty principle \Delta x \Delta p \geq \hbar to find the Bohr radius r_B for a hydrogen atom and the ground state energy E_0. Hint: write down the kinetic...

Homework Statement If the attractive forces between an electron and proton only due to gravity is F=(Gx Me x Mp)/r^2. What is the lowest gravitational Bohr radius? c=2.99799 x 10^8 m/s Me= 9.10939 x 10^-31 Mp=1.67262 x 10^-27 h= 1.05457 x 10^-34 G= 6.67259 x 10^-11 Nm^2/kg^2...

Homework Statement [PLAIN]http://img153.imageshack.us/img153/4822/radiusm.jpg Homework Equations The Attempt at a Solution Using the ratio test: \left | \frac{e^{i(n+1)^2 \theta} \theta^{n+1} z^{(n+1)^2}}{e^{in^2 \theta} \theta ^n z^{n^2}} \right | = | \theta...

Homework Statement The diameters of fine fibers can be accurately measured using interference patterns. Two optically flat pieces of glass that each have a length L are arranged with the fiber between them, as shown below. The setup is illuminated by monochromatic light, and the resulting...

How can I give a fictional planet a realistic mass and surface gravity based on radius? Mercury and Mars are near equal in surface gravity strength, so it does seem that I have some room for variation. From Wikipedia: Earth Average radius 6,371.0 km Surface gravity 9.8 m/s2 Mass...

Gauss's Law - A hollow sphere with inner and outer radius! Homework Statement A spherical shell of inner radius R1 and outer R2 carries a charge Q that is uniformly distributed throughout its volume. No other charges present. a)calculate E inside the sphere b)within the volume c)outside...

Homework Statement There are 3 circles, each tangent to 2 lines and to each other (as in the picture). The radius of the right (largest) circle is 8, and the radius of the left (smallest) circle is 4. What is the radius of the middle circle? The Attempt at a Solution I tried using...

Homework Statement A golfer hits a golf ball from point A with an initial velocity of 50 m/s at an angle of 25° with the horizontal. Determine the radius of curvature of the trajectory described by the ball (a) at point A, (b) at the highest point of the trajectory.Homework Equations p = V2/an...

Homework Statement Say you have a sphere of radius r centered at the origin, and a vector v <r,0,0>. Let v' be the vector v rotated about the y-axis by angle theta. What is the shortest distance between the end of the vector and the z-axis? Homework Equations The Attempt at a Solution I...

Homework Statement Find the radius of convergence of the power series: a) \sum z^{n!} n=0 to infinity b) \sum (n+2^{n})z^{n} n=0 to infinity Homework Equations Radius = 1/(limsup n=>infinity |cn|^1/n) The Attempt at a Solution a) Is cn in this case just 1? And plugging it in...

Homework Statement S = theta * radius I don't understand how they came up with this formula... can some one show me the proof how they derived this formula or can someone send me a link and I will just read it. Thank you. Homework Equations The Attempt at a Solution

Hello all, We know that for some well-behaved, smooth/continuous, twice differentiable function of x, f[x] there exists at each point a slope (f ' [x]) and a radius of curvature \rho [x]=\frac{\left(1+f'[x]^2\right)^{\frac{3}{2}}}{f\text{''}[x]} It also seems intuitive to think that at...

Homework Statement A positively charged Helium atom has two protons in the nucleus and one electron in the shell, in a classic model of the atom, this electron is in a circular orbit around the nucleus with an angular momentum of 4.718x10^-34 Js. What is the radius of the orbit?Homework...

Homework Statement It is found (through and error) that you will "feel" weightless when you travela round at 42 mph over a smoothy rounded hill. What is the radius of the hill? Homework Equations I'm not sure what equation to use with this problem The Attempt at a Solution the...

Homework Statement You have been hired to design a roller coaster and are working on two sections. The roller coaster rolls on the track, but is not attached. If the cars will have a speed of 35 m/s at the bottom of the hill, what is the radius that the circular bottom section of the...

what is the radius of curvature of a parabola y^2=4ax at the end of the focal chord ?

Hey all, I posted this in a thread with similar discussions but thought to make a new one. Skip to the last two sections if you're in a rush :) About me ------------ I did maths in high school and stats in university but I can't work some (probably elementary) sin / cos / tan stuff out...

We did a experiment, and the aim was to find out that relationship between mass and radius with period of time in the circular motion..Although I know the formula for centripetal force, but I am not sure about what the expression should be The lab data : Table 1: 1st experiment ...

First of all, sorry for bad english. Second of all sorry if such thread is already created, but I really need fast help.Homework Statement There's a lamp in the bottom of the lake. If you watch the lamp from the surface(out of the water) and your eyesight is crossed with the lake, you can see...

Homework Statement how to find the radius of curvature for following curve-: x^2y=a(x^2+y^2) at the point (-2a,2a) Homework Equations radius of curvature= {(1+y1)^3/2}/y2 where y1 and y2 are the first and second order...

Hi, So according to the Thomas-Fermi theory, the formula for atomic radius is R=Z^(-1/3)*(hbar ^2)/m*e^2. (in other words Z^(-1/3) times the Bohr radius) While the total energy has a Z^(7/3) dependence. I need to get this from dimensional analysis. I can get the dependence on h, m, and...

Does anyone know how to even start this problem.. :( I seriously have no idea...spent like few hours to find this out on the library and no luck... Please help a poor guy out...I aint smart enough for this...

Homework Statement Find the series' radius and interval of convergence. What what value of x does the series converge absolutely, conditionally? Sum (n=0 to infinity) (nx^n)/((4^n)((n^2) +1))) Homework Equations The Attempt at a Solution Not quite sure where to start with this...

Homework Statement I'm having difficulty obtaining an accurate value possibly due to unit conversions. Homework Equations r_m=mdot/(2*pi*U*N) r_m=mean radius, ft mdot=mass flow rate, lbm/s U= blade velocity, ft/s N= RPM The Attempt at a Solution I know that I have to convert Rpm...

Homework Statement Determine the radius of a highway curve which has a banking angle of 6% over which vehicles will travel at 120km/h Homework Equations I've started with: Fx = -Fcentripetal = (mv2)/r = -Fnsin6 (mv2)/2 = mgsin6 converted my km/h => m/s ... 33.3m/s The...

Homework Statement I'm attempting to find the orbital radius for a binary system based on the parallax of the system and angular seperation: 1. A visual binary system that is 5 pc away is seen edge-on (i.e. we are in the plane of the orbit). The maximum angular separation of the two stars is...

A few days ago I got really excited when I found the equation for a retangles radius (distance from its center to its perimeter given an angle) I have no idea if this is something very simple and stupid but my math teacher said it was impressive, I'm still in high school It's like this...

Homework Statement "The third turn at the Alamo Cart Dirt Speedway is tilted at 30* and has a radius of 240m. Determine the speed of the Cart Car going around the turn, assuming the car has no help from friction." P.S.: This is not a homework or problem worth any credit. Just an extra...

Homework Statement A water tank the shape of an inverted circular cone with a base radius of 2m and height of 4m. if water is being pumped into the tank at a rate of 2m^3/min, find the rate at which the water level is rising when the water is 3m deep. dv/dt = 2m^3/min h = 3m r = h/2...

Some places say (including this paper) claim the bohr radius of muonic hydrogen is 285http://ethesis.unifr.ch/theses/downloads.php?file=LudhovaL.pdf Many more peer reviewed papers say it is 256 fm, or 255 fm though. (search for '256 fm muonic' in teh googlez). So who is right? And more...

Homework Statement What is the mass of a planet (in kg and in percent of the mass of the sun), if: its period is 3.09 days, the radius of the circular orbit is 6.43E9 m, and the orbital velocity is 151 km/s.Homework Equations I'm unsure what formulas to use, though these seem relevant. F=...

Thanks in advance for anybody who is kind enough to help me. No this isn't for my homework. I am not even enrolled in school. I am doing some calculations for personal research. But I need to know the ground state radius of a muonic hydrogen atom to help prove my theory. I already know the...