Circle Definition and 1000 Threads

Homework Statement Consider the ellipse ##\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1## that encloses the circle ##x^{2}+y^{2}=2x##. Find the values of a and b that minimize the area of the ellipse. Homework Equations ##Area=ab\pi## The Attempt at a Solution I begin by completing the square...

Homework Statement [/B] Your niece finds her father's watch. The light watch chain has a length of 48 cm, and the mass of the watch is 270 g. Your niece swings the watch in a vertical circle, maintaining the speed of the watch at 2.3 m/s. Find the tension in the chain when it makes an angle of...

First of all I don't mean a rotating circumference, but rather a translating one which is also rotating. Like this one: https://www.desmos.com/calculator/4vdymlzgpp just play the p button. I understand that the x component of the movement is: and Y= (where v is the radius, s is the angular...

Homework Statement Someone runs on a circle in the direction of a clock. He goes at constant speed. The circle is put in a xy plane that is centered at the origin. The radius is 10 m. At a certain moment he has a speed of (3i + 3j) m/s. Determine the position at this moment. (in vectorial...

circle: (x+2)^2+y^2=1/2 line: x+2 iv been able to find one point but can't find the other work: 2(x+2)^2 =1/2 divide by 2 on both sides (x+2)^2=1/4 square both sides x+2=.5 subtract 2 x=-3/2 i used that to find the y but that only gives me one point please help

Homework Statement Given a circle with a set diameter, how does one calculate the area of the segment below? Homework Equations The only information available is the diameter (in this particular example it is 14"), You may not use angles. Only the chord length. Thank you for your reply. Miguel

I have a circle, representing Earth with equator drawn on it. I need to draw longitudinal lines on 15 degree, 30 degree, and 60 degrees distance? I am not sure how and from where to measure these angular distances. Thanks.

Homework Statement Two lines passing through a point Μ are tangent to a circle at the points A and B. Through a point С taken on the smaller of the arcs AB, a third tangent is drawn up to its intersection points D and Ε with MA and MB respectively. Prove that (1) the perimeter of ▲DME, and (2)...

0 to 1 in Euclidean space. (1 + 1/n)^n using Euler's Number. 1 to 0 with the circle. How amazing is Euler's Number?!

Homework Statement At which minimum velocity should you throw the ball horizontally if you are standing on a hemispherical rock of radius R so that it at no point touches the rock and lands at the minimum distance from the rock horizontally. Find the expression that solves for initial velocity...

Don't exist formula for the eigenvectors, all right!? Eigenvectors needs be found manually, correct!? But and about the Mohr's circle? This physical/mathematical theory don't define clearly the direction of the eigenvectors (called principal direction) with the eigenvalues (called principal...

How can we find that using calculus

Homework Statement A particle moves with constant speed ν around a circle of radius b, with the circle offset from the origin of coordinates by a distance b so that it is tangential to the y axis. Find the particle's velocity vector in polar coordinates. Homework Equations (dots for time...

This is the question: During a time interval of 5 seconds, an object moves through a half circle with a radius of 10 meters, as shown above. What is the magnitude of the object's velocity during this motion? Note: I do not know how to post the diagram, but it simply shows a curved arrow going...

Is this normal? it doesn't seem correct. The equation for the portion of circle with radius 1 unit in the 1st Quadrant is: ## y = f(x) = \sqrt{1-x^2} ## Domain is 0<x But when I calculate f'(x) I also get ## f'(x) = \sqrt{1-x^2} ## I thought inverse functions always reflect about y=x. Please...

Hey JO. The Hamiltonian is: H= \frac{p_{x}^{2}+p_{y}^{2}}{2m} In quantum Mechanics: \hat{H}=-\frac{\hbar^{2}}{2m}(\frac{\partial^{2}}{\partial x^{2}}+\frac{\partial^{2}}{\partial x^{2}}) In polar coordinates: \hat{H}=-\frac{\hbar^{2}}{2m}( \frac{\partial^{2}}{\partial r^{2}}+\frac{1}{r}...

Homework Statement Find the speed which one needs to impart on an object which is hanging on inelastic spring for it to make one revolution. Homework Equations Newton's Laws of Motion The Attempt at a Solution I have two answers for this problem, can't figure out which one is correct.

Buffon`s needle problem described the probability of crossing a set of parallel lines with a known distance between them by a needle of a known length. What is the probability of crossing a circumference of a circle with a known radius by a needle of a known length? I feel that a simple answer...

Homework Statement I have uploaded necessary image(s) for the question I have successfully accomplished a, but I am not sure how to start b. Homework Equations The sum of the integral paths added up = the desired result. The Attempt at a Solution [/B] So we start with path CR And then go...

I get the dynamics of what the question is asking. What I don't get is how to know what pi/8 is. What I've been doing this entire time is plugging it into the calculator as a fraction, and getting the decimal value of it and comparing it to other values I know. I know that pi radians = 180...

Homework Statement 3 tangents intersect a circle of unknown proportions, forming an equilateral triangle. a) Represent this on a Cartesian Plane, with the center of the circle situated at the origin b) Prove that the intersections with the circle are the midpoints of the tangents (assume the...

Hi, I'm trying to understand how Differentiation and integral works in practice, and would really appreciate some help interpreting this calculation- If we have a circle with Area A=pi*r^2 1) If i want to find the change in Area with respect to radius then dA/dr= 2pi*r2) If I'm told...

How find $\frac{a}{b}$

Homework Statement I was asked to show the circle $x^2$ + $y^2$ +6$x$ -10$y$ +9=0 lies entirely inside circle $x^2$ + $y^2$ +4$x$ -6$y$-48=0... For circle $x^2$ + $y^2$ +6$x$ -10$y$ +9=0 I managed to get the centre = (3,5) r=5 For circle $x^2$ + $y^2$ +4$x$ -6$y$-48=0 i gt centre = (2,3) r=...

Since pi is irrational does that mean that a perfect circle could never be produced? Wouldn't a circle be like limit where the ratio of diameter to circumference approaches pi the radius should be the same in any direction.

http://aleph0.clarku.edu/~djoyce/java/elements/bookIV/propIV7.html I was just wondering something . We know that if a line touches a circle at one point, then this means that this line is forming a right angle with the diameter of the circle. (“From this it is clear that the straight line drawn...

Hi. Unfortunately, it looks like my first ever PhysicsForums post isn't even about Physics. I'll think of a Physics-related question later. :) Anyway, I know that each ellipse has an inscribed circle and a circumscribed circle, but I was wondering about a third circle associated with an...

Using the standard equation of a circle x^2 + y^2 = r^2, I took the first and second derivatives and obtained -x/y and -r^2/y^3 , respectively. I understand that the slope is going to be different at each point along the circle, but what does not make sense to me is that the rate of change of...

Mod note: Moved from technical math section, so no template. The diameter of a circle has endpoints P(0,0) and Q(8,-4) Find the equation: First I will find the midpoint: M(x,y)=(x1+x2)/2,(y1+y2)/2 =8/2,-4/2) M(x,y)=(-4,-2) Then I will find the radius: r^2=(x-h)^2+(y-k)^2 r^2=(0-4)^2+(0+2)^2...

Mod note: Moved from technical math section, so no template. Hi All, i couldn't find any geometry under coursework and homework, but saw some geometry under general math. I hope this is the right place, please advise and move if I have posted in the wrong place.The circle with equation...

In the euclidean plane, point A is on a circle centered at point O and point O is on a circle centered at point A. What is measure of angel BAC? So I drew a picture, and it seems that BAC is going to definitely be greater than 90 degree's. From there I am confused on what to do next. Anyone...

There are plenty of proofs for the statement, but I do not find one which is not rely on other assumptions. Here are some common proofs of this statement: https://en.m.wikipedia.org/wiki/Great_Circle#Derivation_of_shortest_paths This proof require the path to be differentiable, which is not a...

Homework Statement Given a randomly drawn circle on a sphere, calculate the probability that it will pass within a defined distance of a set point. To make it clear, imagine the example of the the Earth and Mt Everest. What is the probability that a randomly drawn circle will come within, say...

I have a problem with question 4 part (iv) which is on here http://www.mei.org.uk/files/papers/m208ju_ail7.pdf Basically, I used Ep(initial) + Ek(initial) + W(Forward) = Ep(Final) + Ek(final) + W(Resistive) equation, where Ep is the potential energy, Ek the kinetic energy and W is the work...

Hi Assume an x-coordinate from the unit circle is picked from a uniform distribution. This is the outcome of the random variable X with probability density function Xden(x) = 0.5 (-1 < x < 1). The random variable Y is related to the random variable X by Y = f(X) = √(1-X2) and X = g(Y) =...

Homework Statement If the line ## hk + ky = 1 ## touches the circle ## x^2 + y^2 = a^2 ##, then locus of the points (h,k) is a circle of radius : a h k 1/a Homework Equations NA The Attempt at a Solution Tried differentiating circle equation (Is differentiation of use here?, also don't know if...

In my textbook, its given that the equation of family of circles touching a given circle S and line L is ##S+\lambda L=0## So to find the equation of family of circles touching line L at point P(p,q), can i use the same equation taking S to be a circle of radius zero and center at P? That is...

I am trying to determine the optimum length of the control vectors for a cubic Bézier approximation of a $90^\circ$ circular arc. However to my limited mathematical mind the equation cannot be solved algebraically. Wolfram Alpha even finds it too complicated. However I am told that it IS...

Hi guys, was wondering if anyone could help me solve this problem. Thanks!

At D, by resolving and equating to centripetal force we know that R + W = mv^2/r, however, why do we assume R=0? Based on what? I know my post is short and usually a longer solution is required but I do not have a problem with the maths in the attached, it's just the concept of letting R=0 that...

Homework Statement I have the function f(x) = cos(2x+1) I need to resolve f(x) = 0.6 when -PI <= x <= PI then put my answers in a Trigonometric Circle Homework EquationsThe Attempt at a Solution First I do this: cos(2x+1) = 0.6 and use my TI calculator to solve for X and I find the following...

Can someone explain why the angle inside the triangle inside Mohr's circle is θP2 rather than θP1 ? I understand everything else but just this small point is frustrating me. Thanks

Homework Statement A stone, attached to one end of an inelastic string whirls around in a vertical circle of 1.0 m radius. The tension in the string when the stone is at the bottom of the circle is found to be four times the tension in the string when the stone is at the top. Find the velocity...

Hello, I'm 14 years old and haven't had a lot of physics so please don't say my question is dumb. If you spin a circle the inside travels less distance in the same time the outside does. If you have a really big cirlce can the outside reach the speed of light? I've read somewhere nothing can go...

Hi my name is Jose and I really need to know how to solve a circle as in finding the length of an arc, inscribed angle, and so on... can someone help me?

hi, i'm a newbie... i have this problem: i have a sphere with known and constant R (obvious), i have two point with spherical coordinates P1=(R,p_1,t_1) and P0=(R, p_0, t_0) p_x = phi x = latitude x t_x = theta x =longitude x the distance between point is D=...

Homework Statement An amusement ride consists of a car moving in a vertical circle on the end of a rigid boom. The radius of the circle is 10 m. The combined weight of the car and riders is 5.0 kN. At the top of the circle the car has a speed of 5.0 m/s which is not changing at that instant...

Question: A streetcar is freely coasting (no friction) around a large circular track. It is then switched to a small circular track. When coasting on the smaller circle its speed is: a) greater b) less c) unchanged Relevant Formulas: w = v/r KE = 1/2mv2 My teacher said the normal force from...

A sad and strange image, I know, but better than none at all. What you see is a stake I'm trying to model using CAD software. With the dimension given (5 inches--in case it's not clear, the distance from the top of the equilateral triangle that encloses this shape to the midpoint of the red arc)...

I want to find out the co-ordinate of point of contact of tangent to a circle from external point when its center and radius are known. Please Help me . . . Thank you in advance . . .