Circle Definition and 1000 Threads

Does anyone know if there is a non-Euclidean geometry(or something like that) where the circle becomes a line or a pair of parallel lines? ...or even where the circle becomes a set of parallel lines? ...i'm doing some work in Guitar Theory and this situation appears... Thanks The...

Homework Statement A fly sitting on the end of the second hand of a clock is traveling in a circle. The second hand has a length of 25 cm. Calculate the average acceleration of the fly. Homework Equations The Attempt at a Solution\ since only one measurment is given who would i calculate for...

Homework Statement If \frac{z}{z + 3} is purely imaginary, show that z lies on a certain circle and find the equation of that circle.The Attempt at a Solution So, \frac{z}{z + 3} = \frac{x + iy}{x + iy + 3} Multiplying by the complex conjugate (and simplifying), we get, \frac{x^{2} + y^{2}...

Homework Statement Given the unit circle (in the Euclidean plane) centered at the origin x^2+y^2=1, and a general circle D with equation (x-a)^2+(y-b)^2=c^2 that does not pass through the origin (ie the center of inversion, ie a^2+b^2≠c^2, prove analytically that the inversion of D in the...

I am studying for a test coming up in a few weeks, so what I generally do is be familiar with every aspect of the question. Anyways, going back to the old swinging a pale of water in circular motion example. The force of tension and gravity would be the forces keeping the bucket in circular...

Homework Statement A circle of maximal area is inscribed in the region bounded by the graph of y = -x^2-7x+12 and the x axis. The radius of this circle is of the form (sqrt(p) + q)/r where, p, q and r are integers and are relatively prime.What is p+q+r Homework Equations Vertex form...

Homework Statement Consider the track shown in the figure. The section AB is one quadrant of a circle of radius 2.0 and is frictionless. B to C is a horizontal span 3.5 long with a coefficient of kinetic friction = 0.27. The section CD under the spring is frictionless. A block of mass 1.0...

The ancient problem of squaring the circle is to find a square with the exact area of a given circle. I don't see why this problem is so hard. Say a circle has radius 5. All you have to do is √(∏25) Then that's the length of the side of the square. Help me out here. Why is that not a...

In my Trig class, we learned about the unit circle and its relationship to the various trig functions (sin, cos, etc.). I am curious to know why the unit circle works the way it does, and the how it was "derived" so to speak. More specifically, why does radius of the circle have to be 1 for...

Hi! This is my first time on Physics Forum. (which shows how desperate I am on figuring out this question). Homework Statement r(t) = <3sin(t),4cos(t)> There is a unique circle with the following properties: 1. It passes through the point r(∏/2) 2. At the point r(∏/2), the tangent...

Hi All, I am working on the problem of bead on wire and got stuck on some basic derivation detail. I took the same approach as Andrew Witkin used in his slide (page 13): http://www.cs.cmu.edu/~baraff/sigcourse/slidesf.pdf Here is the screenshot of the slide page 13...

Homework Statement Hi everyone and thank you in advance for your time. I just had this problem on a physics exam (that everyone in the class bombed, and I mean everyone, including the best students). I honestly couldn't care less about the grade, but I really want to understand where I went...

Homework Statement The Attempt at a Solution I understand how to get the derivatives for velocity and acceleration but when the book plugs in the numbers I disagree. velocity at pi 2 sin pi/2 = 0 2 cos pi/2 = -1j therefore, 0 + - 1j = -1j (the books says -2i) velocity at (3pi)/2 2 sin...

Ok I can do the integral and see that it is equal to 2∏i, but thinking about it in terms of 'adding up' all the points along the curve I feel like every every point gets canceled out by its antipode, e.g. 1/i and -1/i.

i am trying to figure out how to calculate the circumference of a circle in the Poincare Half Plane. I know that vertical lines are geodesics so using the arclength formula, the distance between 2 points (x_0, y_0) and (x_1, y_1) on a vertical line is ln(y_1/y_0) . Thus, if i have a circle...

Homework Statement A 1400kg car is driving at a constant velocity, 5.3 m/s. It turns 90 degrees in 4.6 seconds. And then it slams into a tree and it takes 350 ms to stop the car. What is the impulse on the car (a) due to the turn? (b)Due to the collision with the tree? What is the...

Hello, How would you calculate the impulse during the time which a car drives in a circle. You are given the car's mass and constant velocity and the time that the car was turning and how many degrees the car turned. Thanks in advance!

Homework Statement A circuit consists of 7 sections of wire. The figure looks like a rectangle of length 9cm and width 5cm with a circle of diameter 3 cm cutting right through the middle of one of the 9cm sides so that the two sides of the circle are in parallel. Each of the sections of wire...

Gamma is a circle of radius 2 oriented counterclockwise. $$ \int_{\gamma}\frac{dz}{z^2+1} = \int_{\gamma} = \frac{i}{2}\left[\int_{\gamma}\frac{1}{z+i}dz-\int_{\gamma}\frac{1}{z-i}dz\right] $$ $\gamma(t) = 2e^{it}, \ \ \gamma'(t) = 2ie^{it}$ $$ \int_{\gamma}\frac{2ie^{it}}{2e^{it}+i}dz $$...

Homework Statement A quarter circle segment has a uniform linear charge density of λ. Starting with the E-field due to point charges, show that the magnitude of the E-field at the center of curvature(which is distance R away from all points on the quarter circle) is E= (kλ√(2))/R Homework...

So my problem is this: I need to figure out the center of a circle given two points. At one of the points, I know the tangent angle. So I know (x1, y1, θ1) and (x2, y2) and need to find (xc, yc). I also need to do this on a computer so I need some sort of closed-form solution. The way I...

Homework Statement A block of mass m1=2kg is attached to a cord. The cord goes down through a hole in the table and is attached to mass m2=4 kg hanging below the table. The 2 kg mass moves on the table in a circle at a speed of 3.5 m/s the table top is friction less and there is no friction...

Homework Statement A block of mass m1=2kg is attached to a cord. The cord goes down through a hole in the table and is attached to mass m2=4 kg hanging below the table. The 2 kg mass moves on the table in a circle at a speed of 3.5 m/s the table top is friction less and there is no friction...

Homework Statement 1. Homework Statement A block of mass 0.015kg enters the bottom of a circular, vertical track with a radius R = 0.3m at an initial velocity of 4/ms. If the block loses contact with the track at an angle of 130 degrees, what is Wk, the work done by kinetic friction...

Homework Statement A block of mass 15g enters the bottom of a circular, vertical track with a radius R = 0.5m at an initial velocity of 4/ms. If the block loses contact with the track at an angle of  = 130, what is Wk, the work done by kinetic friction...

gamma is a circle of radius 2, centered at the origin, and oriented counterclockwise $\displaystyle\int_{\gamma}\frac{dz}{z^2+1} =\int_{\gamma}\frac{dz}{(z+i)(z-i)}=\frac{1}{2}\int_{\gamma}\frac{\frac{1}{z-i}}{z-(-i)}dz+\int_{\gamma}\frac{\frac{1}{z+i}}{z-i}dz = 4\pi...

What does it mean to find the area? I've read somewhere and the person says, it means to find the space enclosed, but I still don't know what that means. I understand what area intuitively means, but not logically.

Homework Statement there is a cylindrical area in xy plane with a magnetic field (into the plane) that changes with time like that: (dB/dt)=δ the magnetic field outside the area is 0. the radius of the cylinder is a. we pick a string in the circle with lentgh L which is smaller than the...

Homework Statement Find the distance from Atlanta to San Francisco if Atlanta is @ 33.75°N and 84.40°W and San Francisco is @ 37.78°N and 122.42°W. Explain your strategy. Homework Equations cos phi = z/rho cos theta = x/r r = rho*sin phi The Attempt at a Solution I believe that...

Hi all, How do I find the center of a circle given a point (tangent to the circle) and the radius. Thanks, CG

If you have a triangle circumscribed around a circle, how do you find the area of that circle? Say that the triangle is an equilateral triangle with side length of 8 cm. I found the area of the triangle using Heron's formula: 16√3 cm^2. Apparently the answer is 16π/3 cm^2. I'm just confused...

Hi everyone. I hope I've found the right place for my first post here. I have a geometry problem which I need to solve for a piece of software I'm writing, and I'm hoping someone might be able to help me. I have a non-rotated ellipse inside a circle, as in this diagram. I know the x and y...

Hi, I've researched this problem all across the web and most answers involve finding the distance between two points on a great circle, mostly in nautical terms, using latitude and longitude, etc. but that isn't the answer I'm looking for. It's generally agreed if you have two points on a...

How would I analize a bolt in tension and shear. Imagine an "L" bracket bolted in the configuration below "||" represents a bolt. There is a force "<--" at the top of the bracket. <--| ...| ...|_____||_ The bolt will see tension and shear. There will be tension in the y direction (Sigma...

Homework Statement By employing spherical polar coordinates show that the circumference C of a circle of radius R inscribed on a sphere S^{2} obeys the inequality C<2\piR The Attempt at a Solution I proved C=2\piR\sqrt{1-\frac{R^2}{4r^2}} So if r>R, then the equality is correct. Am I right...

Mentor comment: Harmony360 original post violated our rules. The new wording is mine. D H[/color] So, why there are 360 degress in a circle?

How could i mathematically proove that I am living on a circle. Almost got it last night , just need an insight to figure out an equation. Ty.

Homework Statement A ball on top of a circle is acted on by a FG. The ball rolls to a certain point on the circle, and detaches. Ffr Is negligable. Given info: Diameter Of the circle, Mass of ball no ffr x = the distance from the balls posistion to the top of the big circle. x is what is...

I'm getting approximations within 5% of the actual values. Does that sound about right?

Homework Statement Write the equation of a circle in complex number notation: The circle through 1, i, and 0. Homework Equations The Attempt at a Solution I know the equation for a circle with complex numbers is of the form |z-a| = r where a is the center point and r is the...

How can I find the radius of a circle by knowing two points and its arc length? Do I have to use a numerical method to solve for a trigonometric equation or is there any algebraic or geometric method?

Homework Statement http://s2.ipicture.ru/uploads/20120107/67Ag24Qb.jpg The attempt at a solution So, i plotted the graphs of the circle and the curve: http://s2.ipicture.ru/uploads/20120107/x32KTV6y.jpg The shaded area is what i need to find. My plan to solve this problem is to find...

Hi there, I am trying to understand calculus as concerns circles and I can clearly see that the integral of a circumference is an area: \int2∏r = ∏r^{2} but what do I get if I integrate the area, I get ∏r^{3}/3 I am confused as to what this shape would be, I kind of was expecting a...

I'm just wondering about using a Mohr's Circle, do I need to use the same scale for the x and y axes, as surely otherwise my choice of scale greatly impacts the results. I am using one to get my principle second moment of areas, Ix and Iy, for an equal L section. Ix and Iy are where the...

Homework Statement A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ft/s. Does the area also increase at a constant rate? Homework Equations A = ∏r2 The Attempt at a Solution dA/dt = 2∏r(dr/dt) dA/dt = 2∏r(3ft/s) What now?

Homework Statement --SOLVED-- It seems, that you just apply the pythageos thereom to 'A' and 'B' =)--------------- Lets say I have a circle 'A' with radius 6cm, and a circle 'B' with radius 6cm. These two circles would have an area of 113.097cm^2. When both are combined they would have an...

Hey guys, New here. It's been a while since I've done any physics. I've been playing around with some mental work in my head and I am trying to figure out why something doesn't work. I know it shouldn't work, but I can't figure out the why. What I am talking about is utilizing similar charges...

[SIZE="1"]Sorry for my lack of knowledge, I'm in Grade 7 I just learned that Magnets have dipoles--like this: If those dipoles formed a circle, wouldn't it be possible to create perpetual motion?

Homework Statement PICTURE: http://imageshack.us/photo/my-images/21/circls.png/ A Force of gravity acts upon a ball on top a circle. The ball rolls a down the curve of the circle until a CERTAIN POINT. at this CERTAIN POINT the ball detaches from the circle and travels until it his the ground...

This is my first post here and any help is appreciated. I belong to a drag racing forum and this has been a hot topic of discussion. If you have a 4 inch round pipe by 2 inches tall and insert the pipe into a vice and make it oval shaped it would somehow change the volume. Please see...