Circle Definition and 1000 Threads

So I always wondered why you multiply by pi when you're finding an area of a circle, for a rectangle you multiply by length and width, I guess that makes sense... How I see multiplying a length and width is if you have a length of 5 cm and a width of 4 cm, I imagine you just stack 4, 5 cm...

Hi. I want to know the equation to draw a circle that's a bit tilted. Imagine a 3D circle that's parallel with the Y axis. Now I want to take that circle and have its center cross through the origin still, but I want it to be θ degrees titled from the Y Axis. I'm using the following...

Homework Statement A wagon is drawn by a student pulling with a constant force of F Newtons applied at an angle of θ° to the horizontal. If the wagon is drawn in a circle with radius r meters, how much work is done on the wagon? (I don't remember the actual numbers) Homework Equations...

my textbook says: "As a gyroscope precesses, its center off mass moves in a circle with radius r in a horizontal plane. Its vertical component of acceleration is zero so the upward normal force exerted by the pivot must equal mg." Now wouldn't this always be true. I mean if u have a...

[SIZE="4"]Circle Rolling around Rolling Circle (1) Circle 1 rolls around inside of the fixed base circle. Circle 2 rolls around inside of Circle 1.

Homework Statement A wire of resistance 8R is bent in the form of a circle. What is the effective resistance between the ends of a diameter AB? Homework Equations I have attached the image and my attempt to solve it as told by my teacher. Homework Equations The Attempt at...

Ball Rolls off of a circle :O! PROBLEM! So the problem is, a ball at zero velocity begins to roll on a circle. At a certain point the ball and the circle "DISCONNECT". There is a height x from the roof to the point it disconnects. Given Information. Height X, Diameter D of circle, Vi=0...

Homework Statement Suppose a slingshot rotates clockwise along the circle x^2 + y^2 = 9 and the rock is released at the point (2.99,0.77). If the rock travels 200 feet, where does it land? Homework Equations The Attempt at a Solution I think you might have to find the tangent at...

http://www.up98.org/upload/server1/01/z/cllb59cvnwaigmmar6b5.jpeg What is the method of calculating arc length in In the image above . x & y is known Thanks .

I was looking at the equation of a circle in polar coordinates on wikipedia, http://en.wikipedia.org/wiki/Polar_coordinate_system and I understand that a is the radius of the circle, and that (r0, phi) is the center of the circle. But I don't see what the r and theta refer to :(.

Prove that angle WTU is twice as large as angle WOX. Any help would be greatly appreciated.

Homework Statement An aluminum wire is 0.850 m long and has a circular cross section of diameter 0.780 mm. Fixed at the top end, the wire supports a 1.20-kg object that swings in a horizontal circle. Determine the angular velocity required to produce a strain of 1.00  10–3. Homework...

Hi I just want to check that I am doing this math problem correctly. We were given a density function for review for an upcoming math test. We were then asked to find the volume in a circular radius given this density function. I will post the exact problem now then explain the steps I...

Homework Statement Find a vector function that parameterizes a curve C which lies in the plane x-y+z=2 and directly above the circle x2 + (y-1)2 = 9 The Attempt at a SolutionSo, in order to parameterize the circle, I simply use x=cos(t), y = sin(t) with some adjustments. Namely, I let...

Homework Statement Please see below... Homework Equations Please see below... The Attempt at a Solution Hi. This question is on geometry with circle and triangle. I am stuck only on 2 parts of the solution and not the whole solution... Thank you...

Homework Statement Use greens theorem to solve the closed curve line integral: \oint(ydx-xdy) The curve is a circle with its center at origin with a radius of 1. Homework Equations x^2 + y^2 = 1 The Attempt at a Solution Greens theorem states that: Given F=[P,Q]=[y, -x]=yi-xj...

Homework Statement A mass moves in a circular path that has a radius of 24.6cm on a horizontal frictionaless surface. If the centripetal force acting on the mass is 96.5N, what is the kinetic energy of the mass? r=0.246m Fc=96.5N Homework Equations He told us to use these and "play...

Hi, i can not understand how circle has a nontrivial bundle, Möbius bundle. Can you say me what is its transition function on it.

Homework Statement Two equal masses are glued to a massless hoop of radius R that is free to rotate about its center in a vertical plane. The angle between the masses is 2*theta. Find the frequency of small oscillations.Homework Equations \frac{d}{dt} \frac{∂L}{∂\dot{q}}=\frac{∂L}{∂q} The...

There have been a couple of posts over the last few months that posit a relativistic-speed path in a circle around the Earth and I want to make sure I correctly understand the ramifications. It's the twin paradox in a circle. SO ... here's a scenario that I think will solidify it for me: This...

Homework Statement This is me paraphrasing. It's about uniform circular motion. The question involves a pig on a string dangling below a motor. It rotates in a circle below the horizontal. Resolve the tension vector into components. The vertical component of tension is equal to the...

We can express any circle in the complex plane as |z-a|=k|z-b| where a and b are distinct complex numbers, k > 0 and k \not= 1. Is there an elegant way of showing this fundamental property of the complex plane to be true?

The question is: A circle touches the y-axis at the origin and goes through the point A(8, 0). The point C is on the circumference. Find the greatest possible area of ∆OAC I graphed the above situation, and used the equation A=(1/2)bcsinA, but i couldn't muster up an answer. Your...

Let a circle be given by 2x (x-a) + y(2y-b) = 0; (a≠0, b≠0). Find the condition on a and b if two chords, each bisected by the x-axis, can be drawn to the circle from (a, b/2) My attempt in this question is not quite relevant at this moment. I just found that (a,b/2) will lie on circle and...

Alright, this is a bit of a confusing one for me. The problem: The ultimate objective is to get the coordinates of the points on the edge of the rectangle (labeled: (?,?) ), given the angle, and the height and width of the rectangle. The more I think about this problem, however, the more I...

Homework Statement Find the Lagrangian of a simple pendulum of mass m whose point of support moves uniformly on a vertical circle with constant angular velocity. (So basically there is a circle around the origin that spins with a constant angular velocity and the pendulum is attached to the...

Homework Statement Can someone check if this is right? The time seems okay, but the work I feel is wrong A ball with moment of inertia 0.1kg · m2 is rotating on a table, but friction is slowing it down with constant angular acceleration. The ball is originally spinning at 2π radians per...

Homework Statement 9. A 0.61 kg mass attached to the end of a 0.50 m cord rotates in a vertical circle. The angular speed of the mass at the bottom of the circle is 2π rad/s. The tension in the string at this point is: a. 18 N b. 21 N c. 12 N *d. 54 N Homework Equations W=mg F=ma...

Homework Statement This is part from a larger construction, but I realized if i can construct this, i can do the larger construction. All ofcourse with ruler and compass. I have been given an angle with its bisector and a point on that bisector. I have to construct a circle trough that point...

Homework Statement A light string can support a stationary hanging load of 25.0kg before breaking. An object of mass m = 3.00kg attached to the string rotates on a frictionless, horizontal table in a circle of radius r = 0.800m, and the other end of the string is held fixed. What range of...

Homework Statement Define a relation on R as follows. For a,b ∈ R, a ∼ b if a−b ∈ Z. Prove that this is an equivalence relation. Can you identify the set of equivalence classes with the unit circle in a natural way? Homework Equations The Attempt at a Solution I have already proven that this...

Homework Statement I need to get a tricycle to move around a circle (depending on the angle of the front wheel) in MATLAB (but any mathematical formulae would help). I have the variables: M (x, y, theta) which is the center point between the 2 back wheels and the angle of the tricycle, the...

Homework Statement A metal bar of length l in the figure below has one end attached at a point P to a circle ofradius a < l. Point Q at the other end can slide back and forth along the x–axis. (a) Find x as a function of θ (θ=angle POQ). (b) Assume the lengths are in centimeters and the...

Homework Statement The drawing below shows a person who, starting from rest at the top of a cliff, swings down at the end of a rope, releases it, and falls into the water below. There are two paths by which the person can enter the water. Suppose he enters the water at a speed of 10.0 m/s via...

I was wondering if the common chord of two intersecting circles subtends an equal angle in both circles at the circumference (in no special cases i.e different radii circles etc) If not, are there any special case(s) where this would work, making these two triangles similar or ABDC is a...

Hi guys! Excuse the spam, but I would like to ask something which I read in Armstrongs Basic Topology which I am just not 100% sure about. He says we wish to define homeomorphism such that a circle cannot be homeomorphic to an interval such as [0,1). A continuous function f : X \mapsto Y is...

given the x,y coordinates of two points and the radius of a curve. has anyone got a formula for calculating the coordinates of the centre point please

Homework Statement A small block with mass 0.0325 kg slides in a vertical circle of radius 0.475 m on the inside of a circular track. During one of the revolutions of the block, when the block is at the bottom of its path, point A, the magnitude of the normal force exerted on the block by...

Homework Statement A mass of 2kg rotates at 1m/s in a horizontal circle on a table at the end of a spring with an elastic constant of 50N/m. If the original length of the spring is 2m, find the extension of the spring. Given - M=2kg, V=1m/s, k=50N/m, original length of x=2m find x'...

Homework Statement A student ties a 400g rock to a 1.0m long string and swings it around her head in a horizontal circle. What angular speed does the string tilt down at a 10° angle? m = 400g = .4kg r = 1m Homework Equations F = \frac {mv^2}{r} \omega = \frac {|v|sin \theta}{|r|}...

I know, that probably this will sound to be a dumb question but I can't find the solution to it. So if anyone could help please ? Homework Statement In a class of 40 pupils, 18 take Mathematics 19 take History 16 take Art 6 take both Mathematics and History 5 take both History and Art 7 take...

As usual I'm working on a program and I'm having trouble with math/efficiency. Homework Statement I need a way to find out if a circle given as a point and a radius C(x,y,r) fully encloses a rectangle given by the top left corner and the width and height R(x,y,w,h) I only need to know...

When a car is moving on a circular track which is sloped away from the centre of the track, is the static friction keep that car on the circle (constant speed) towards the outside of the circle, opposite the acceleration? I'm having trouble seeing this because to me, the car would want to...

Consider the sequence (n) n=1 to infinity. Plot the sequence on the unit circle: n modulo 2*pi for n≥1. What do you see? Attempt: I really honestly have no idea what to do. We are learning in class about limit laws and how to prove them, so this question seems to be coming out of nowhere. :(

I'm trying to find the equation for a circle given two points in x, y and the starting angle, arc length, and two points along the circle. I need to find the equation because I need to translate a sprite along the curved path from one point to another. The situation ends up looking like this:A...

Homework Statement A ball of mass m is suspended from a rope of length R. The ball is set into freely swinging circular motion a vertical plane. The centripetal acceleration of the ball at the top of the circle is 13g. What is the centripetal acceleration of the ball at the bottom of the...

Homework Statement A point-particle sits at rest at the top of a half-circle with radius R. Find the minimum initial velocity v0 the particle has to have in order to clear the half circle without rolling down on one of its sides. Homework Equations None are given. The Attempt at a...

What I'm looking for is an algorithm to find the details on the intersection of of a circle and rectangle in two dimensional Euclidean space. The information I need to find is straightforward enough; all I need is to know whether the rectangle and circle are not intersecting, partially...

Homework Statement Delegates from the G8 are to be seated around a circular table. How many different seating arrangements are possible if the French and Canadian delegates are to be seated next to each other, but the Russian and Japanese are not to be next to each other? Homework...

Homework Statement The line x+y=2a-1 intersects the circle x2+y2=a2+3a-3 at point (m,n). When m*n reaches its minimum value, what is the value of a?Homework Equations Equation One x + y = 2a - 1 Equation Two x2 + y 2 = a 2 + 3a - 3