Circle Definition and 1000 Threads

A ball is spun in a vertical circle on a string. A light is shining from the side of the circle so that a shadow of the balls motion is shown on a wall behind it. The shadow is simply a circle moving up and down in a straight line (I can't attach the image). The amplitude of the shadow is 0.5m...

Homework Statement if equation of 3 circles is given then find the equation of the smallest circle containing all 3 circles Homework Equations The Attempt at a Solution i can do this question for 2 circles , please give a hint for 3 circles

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...

Hi, I am reading this paper and it has a symbol that I don't know what it's called. So for an x enclosed in a circle, it represents an analog multiplier. What does a "+" enclosed in a circle mean? I know it's add the analog signal, but what is it called?

Years ago my high school math teacher showed us how to find the center of a given circle using only a compass, nothing else. I can't remember how. I need to do it now. Does anyone have the answer?

I'm trying to understand parallel transport and I'm stuck. The example given is if you have a unit sphere and you take one of the latitudes (not the equator), take at a point on the latitude the tangent vector to the curve, and parallel transport it around the curve. I don't understand why the...

I've got a unit sphere sitting at the origin. This sphere is cut by an arbitrary plane. I'm looking to find the equation of the circle that results from the intersection in spherical coordinates. This is for a computer program I'm writing, and I've already set it up to approximate this by...

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...

1. A string 1.5 m long is used to whirl a 1.5 kg stone in a vertical circle to that its velocity at the top is 6 m/s. What if tension in the string when it is horizontal? (g = 9.8 m/s2) 2. Centripetal acceleration = mv^2/r 3. i don't get what they mean by vertical circle...

Find the p-adic volume of the p-adic circle x^2 + y^2 = 1. This isn't hw.

God knows if I'm posting this in the right place on physics forum but here goes... If a circle can be thought of as a shape with an infinite number of sides does this then therefore mean that each side would have to be infinitely small? Within a large circle you can draw a smaller circle...

1. Show that S:= {(x,y)an element of R^2 : x^2 + y^2 =1} is connected. 2. Relevant theorems 1. Path-connected implies connected. The Attempt at a Solution Define f: [0,2pi] --> R^2 by f(x) = (cos(x),sin(x)). This map is continuous, and its image is S^1. The interval [0,2pi]...

Ok- I am teaching trigonometry to low level students right now and I am trying to figure out why they need to know the unit circle. Are there some interesting things they can learn about by using a unit circle? So far, we pretended it was a magic-barbie-sized-half-underground-ferris-wheel...

Hey, I have scoured the interned for an answer to this question, but so far my search has been uneventful. Given a circle with center point (h,k), radius r, and a point on the circle (x,y), I need to find the point on the circle at angle a from (x,y). Any thoughts? Attached is a...

Homework Statement Semi circle of Radius R given. Find center of mass using polar coordinates, not double integrals. Homework Equations .5 intergral(r^2dpheta) (1/M) integral y dm r=R The Attempt at a Solution .5(2/piR^2) integral(R^3sinpheta do pheta) from 0 to pi, when I evaluate it I...

Homework Statement L = R \int \sqrt{1+ sin^2 \theta \phi ' ^ 2} d\theta from theta 1 to theta 2 Using this result, prove that the geodesic (shortest path) between two given points on a sphere is a great circle. [Hint: The integrand f(\phi,\phi',\theta) in the result is independent of...

if you have a quadrant sitting on top of the x-axis and on the right of the y axis, when you draw a line perpendicular to the x-axis that splits the circle into two equal parts, then what is the value of 0 on the x-axis to the line mark when r=2? too bad i don't have a diagram to show you

Homework Statement Given two isotropic point sources of sound \[s_{1}\] and \[s_{2}\]. The sources emit waves in phase at wavelength 0.50m; they are separated by D = 1.75m. If we move a sound detector along a large circle centered at the midpoint between the sources, at how many points do...

Homework Statement Homework Equations d = 2.5 c = pi*d = 7.854 velocity/s ?= c * 2 = 15.7079The Attempt at a Solution Since PR is 1/4 of the circle and the particle moves around the circle 2 times per second, I thought the average velocity would be 1/8th of the velocity that it's traveling...

Hi, I have been told that in R^2 the unit circle {(x,y) | x^2 + y^2 = 1} is smoothly mappable to the curve {(x,y) | x^4 + y^2 = 1}. Can someone please tell me what this smooth map is between them? I can only think of using the map (x,y) --> (sqrt(x), y) if x is non-negative and (sqrt(-x), y)...

Homework Statement As stated abv. Since \pi can only be established by infinite sum and according to zeno's paradox we can never break a finite length into infinite pieces (loosely speaking)

Homework Statement You push an object of mass m slowly, partway up a loop-the-loop track of radius R, starting from the bottom, where the normal force to the track is vertically upward, and ending at a point a height h< R above the bottom. The coefficient of friction between the object and the...

Homework Statement A 2-kilogram block is released from rest at the top of a curved incline in the shape of a quarter circle of radius R. The block then slides onto a horizontal plane where it finally comes to rest 8 meters from the beginning of the plane. The curved incline is frictionless...

Homework Statement parameterize the following a circle with radius 2 , centered at 1,2,3 and lies on the plane x+y+z=6 The Attempt at a Solution ok i think i know how to get radius 2, centered 1,2,3 namely, r(t) = (1,2,3) + (2cos(t),2sin(t),t) but how do i fit into the plane...

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 Twelve identical point charges are equally spaced around the circumference of a circle of radius 'R'. The circle is centered at the origin. One of the twelve charges, which happens to be on the positive axis, is now moved to the center of the circle. Part A Find the...

when a particle is constraint to move on a circle, what are the constraint forces

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...

the question: if a straight line c(-*81/2,-*81/2) making an angle 135 dge with x-axis,cuts the circle x=5cosm y=5sinm in points A and B ,find length of segment AB . in the equation of line by solving i got y=-x and tried to solve and ended up getting length of AB as 0 but the solution has...

A circle with diameter 90 is located at (70,100). A given point O is at (0,0). There is a line from O to the circle at point A, line OA. Line BT is parallel to OA at a distance 50 from OA and is a tangent to the circle. How do I find the coordinates A and B? I'm having problems drawing...

Homework Statement Today we went over finding the arc length s of a circle with a given radian and radius... Thus s = radian*radius... Thats easy to remember but I think it will be more memorable for the long run if I knew the proof and understood it... can some one please post a website...

Homework Statement Here is a diagram: http://i55.tinypic.com/k18g14.jpg A ball of mass 0.75 kg on the end of a cord is swung in a circle of radius 1.5 m with a period of 1.5 s as shown in the diagram. a.) What is the speed of the ball? b.) What is the acceleration of the ball? c.) What...

I'm sure this is something so simple, but I've failed to find answer elsewhere, even doing several google searches "circle on circuit board", "diagram of circuit", etc... What is the circle at the end of a wire\line on a circuit board? (the actual circuit board, not a diagram\drawing of one)...

Homework Statement The circle x2 + y2 - 4x - 4y + 4 = 0 is inscribed in a triangle, which has two of its sides along the coordinate axes. If the locus of the circumcentre is of the form x + y - xy + k(x2 + y2)1/2= 0. Find k.The Attempt at a Solution The centre of the given circle is (2,2) and...

This is something I have zero familiarity with. Anyways, I was given the equation: r=2asin(theta)+2bcos(theta) and had to prove that it was a circle, and then state its center in cartesian and cylindrical coordinates. After making the appropriate substitutions and completing the square...

The book talks about a unit circle... 360 deg = 2(pi) rad if it wasnt a unit circle... say r = 4 would it then be 360 deg = 8(pi) rad?

How does the function f(z) = z + 1/z take a circle of radius g.t. 1 to an ellipse? How do I think about it geometrically ? (i.e., how should I be able to look at the complex function and tell straight away)

Homework Statement consider the family of complex mappings: z -> Ma(z) = (z-a)/(áz-1) (a constant) (á is complex conjugate of a) Show that Ma(z) maps the unit circle to itself.Homework Equations the solution should look something like this i guess: Ma(ei*alpha) = ei*alpha The Attempt at a...

I am looking to bypass an existing sewer pipe with another pipe. The existing pipe is rectangular, approximately 9'x5'. I am looking to use a circular bypass pipe of 6' diameter. Since the velocity of "water" flowing thru the pipe will be the same then I need to compare the surface areas...

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...

hello, I've posted this question on a math forum, but they weren't much help - this really is more appropriate in physics ;) i'm working on a computer program and I'm using a library that generates a 2D graphics of a circle given a theta and phi. if i want to make the ball rotate around its...

Lets say i draw a circle, and then from the center i draw a line to the outer edge and let's say i do this for every point on the line. So I've gone completely around the circle. I should have an infinite amount of lines . And now let's say i draw a bigger circle around that and then extend...

Homework Statement A metal ball is attached to a rope with length 2.40 m and swung in constant velocity in a circle with velocity 3.0 m/s A light at the same height casts a shadow from the center to 0.8 m, what is the velocity at this point?Homework Equations The Attempt at a Solution

Hello. For a physics course, I need to often make use of the binomial series and it's corollary, the expansion of: \sqrt{1-x^2} This probably sounds rather stupid, but for some reason, when I do a MacClaurin expansion of this series, I cannot seem to generate the correct series, which I...

Homework Statement Choose a point in the unit axis, say x.Let Y be the distance of that point and the point where thε perpendicular line crosses the unit circle. Find the density and cumulative functions of Y. Homework Equations Basic trigonometry i guess. The Attempt at a Solution...

In a lot of physics book there is an example of a problem saying that we tie a bucket of water to a string and move it with vertical circular motion what is the minimum speed ,and the way they told us to solve these problem is to set the normal force to 0 then solve for v ,but I never actually...

Does anyone know the (x,y) solutions on the unit circle for 15, 75, 105, 165, 195, 255, 285, or 345 degrees?

Hello there, suppose i want to find the arc length of a circle x^2+y^2=R^2 using integration, implicitly differentiating the equation, i find y'=-(x/y) now, arc length (circumference)= (\int \sqrt{1+y'^2}dx putting the value of y'=-(x/y) and substituting for y^2 from the equation of the...

What is the symbol of an integral with a circle in the middle called? I am asking because Gauss's Law is defined to be equal to that integral of the dot product of E and dA.

Homework Statement Parametrize a circle of radius r on a sphere of radius R>r by arclength. Homework Equations Circle Equation: (cos [theta], sin[theta], 0) The Attempt at a Solution I don't know if the professor is tricking us, but isn't the parametrization just Circle...