Circle Definition and 1000 Threads

So, the values of polynomial ##p## on the complex unit circle can be written as ##\displaystyle p(e^{i\theta}) = a_0 + a_1 e^{i\theta} + a_2 e^{2i\theta} + \dots + a_n e^{ni\theta}##. (*) If I also write ##\displaystyle a_k = |a_k |e^{i\theta_k}##, then the complex phases of the RHS terms of...

I was wondering how one can calculate the radius of the circle a car will follow if it turns its wheels a given angle to its current velocity? For example, if i turn the wheels of my car by 12 degrees to my current direction, how large of a circle will the car perform

At the bottom of the circle, the tension force is greater than the weight force as there must be a net force acting towards the centre to provide the centripetal force causing the centripetal acceleration and thus the circular motion. In the equation above (T = mv^2/r + mg) I only have the mass...

I have been trying to see if my understanding of uncertainty principle is right. So I thought consider a circle. for this augment we will look at its diameter and it circumference. Suppose you get a length of string and make a exact measure of the circles circumference using this length of...

I have tried a lot by angle chasing e.g. let ∠ABC=x° then ∠ACB=90°-x°. As AU=AV=radius of circle so ∠AUV=∠AVU=45°. I've connected U,D and V,D. Then ∠UDV=135° etc. But I haven't found any way to get near of proving AE=DE. I have also tried to prove 'the area of triangle AEU= area of triangle...

##AD## is diameter, thus ##\angle ACD = \angle ABD = 90^\circ##. Also ##HBDC## is a parallelogram because ##HC||BD, HB||CD##. It seems useless and I don't know how to continue. Thank you in advance!

A circle is inscribed in a square with sides = 40. A smaller (of course!) circle tangent to the above circle and 2 sides of the square is inscribed in one of the corners of the square. What is the diameter of this circle?

This is my attempt at a solution. Point A is the center of the circle (6,8) and Point B is the given point (12,16). I believe that the shortest path would be the one that is equal to the sum of CE and EB or its symmetrical complement. (I forgot to put a point where the top line intersects the...

Say "I have grid in polar coordinates (r, theta). How do I plot it in tecplot. Tecplot plots it in cartesian coordinates."

https://en.wikipedia.org/wiki/Area_of_a_circle#Onion_proof I understand the basic concept, although it is a little difficult to visualize the thin discs close to the centre of the circle. Regarding the area of each disc, it is given in the link above as 2πrdr. Then, by means of integration...

Homework Statement Imagine an infinite straight wire pointing at you (thus, the magnetic field curls counterclockwise from your perspective). Such a magnetic field equals to: $$B = \frac{\mu I}{2 \pi s} \hat{\phi}$$ I want to calculate the line integral of ##B## around the circular path of...

Hi all, this is my first thread! I am having problems trying to find the way of drawing a line which is tangent to a circle and intersects another circle making a 30º intersection. Let´s say I have circle A with coordinates 479183.87, 4365099.87 (x1,y1) and a radius of 27780m. I have a second...

Homework Statement Finding the general formula for max angular velocity ( answers say 0.839*(g/b)) but I do not understand how Homework Equations 0.839*(g/b) The Attempt at a Solution

Homework Statement Calculate the circumference (including uncertainty) of a circle whose measured radius is r=7.3 ± 0.2cm. 2.Relevant equations & 3.The attempt at a solution - Circumference of circle --> C = 2πr = 2π7.3 = 45.87 cm - Exact constant error propagation --> z =...

Hi. I have just looked at a question concerning a free particle on a circle with ψ(0) = ψ(L). The question asks to find a self-adjoint operator that commutes with H but not p. Because H commutes with p , i assumed there was no such operator. The answer given , was the parity operator. It acts...

A 0.160 kg ball attached to a light cord is swung in a vertical circle of radius 70.0 cm. At the top of the swing, the speed of the ball is 3.26 m/s. The centre of the circle is 1.50 m above the floor. a. Draw a free-body diagram of the forces on the ball at the top of the swing. b. Calculate...

Hi PF! Given a 2D plane, the following is a parameterization of a circular arc with contact angle ##\alpha## to the x-axis: $$\left\langle \frac{\sin s}{\sin\alpha},\frac{\cos s - \cos\alpha}{\sin\alpha} \right\rangle : s \in [-\alpha,\alpha]$$ However, I am trying to parameterize a circle...

Say there is a circular fence that has a diameter of 10 meters, and a rocket ship that is normally 20 meters goes very quickly so that its relativistic length is 1m from the position of an observer standing at rest with relation to the fence. The rocket ship starts to go in a circle inside the...

Im having a bit of trouble when it comes to what the abstract object S1 actually is. Often in a book they will mention a parametrization of the circle in the complex or real plane. But this requires embedding the circle in Euclidian space. How should one think of the object S1 without thinking...

So far i have. 14) area of sector is πr²/3 = 12π length of chord. that triangle has two sides of 6 and angle of 120º split the triangle in two right triangles with angle of 120/2 = 60 and hyp=6. other (longer) side is: sin 60 = x/6 s = 6 sin 60 = 6(√3/2) = 3√3 third side is s = 3 cos 60 =...

So far i have 270/360× (pi)r^ i don't know what to do next please help.

So I've been able to solve A.12 inch B.24 inch C.75.3982 D.452.389 Cant solve e. Arc length can anyone please explain the formula. Thank you

Homework Statement Equation of the circle passing through the point (1,2) and (3,4) and touching the line 3x+y-3=0 is? Homework Equations x^2+y^2+2gx+2fy+c=0...(1) (-g,-f)=center of circle sqrt(g^2+f^2-c)=radius...(2) The Attempt at a Solution Putting (1,2) and (3,4) in equation 1 we get...

I am reading the book: "Vector Calculus, Linear Algebra and Differential Forms" (Fourth Edition) by John H Hubbard and Barbara Burke Hubbard. I am currently focused on Section 3.1: Manifolds ... I need some help in order to understand Example 3.1.3 ... ... Example 3.1.3 reads as follows:In...

Homework Statement You swing a 1.60m long string with a metal ball attached to its end in a vertical circle, such that the speed of the ball does not change but the rope is always taut. The tension in the string when the ball is at the bottom of the circle is 60.0N more than the tension when...

Hey! :o I am looking at an exercise that is formulated as follows: Finite number k of squares on a circular route. The whole fuel in all is enough for 1 circle. Show that there is a way to integrate the circle however the squares and the fuel are distributed. There is also the following...

Without a calculator, find all solutions w between 0 and 360, inclusive, providing diagrams that support your results. 1) cosW=sin20 2) sinW=cos(-10) 3) sinW< 0.5 4) 1<tanW

Homework Statement :[/B] One swings a rock at the end of a string. We wish for the string to remain taut and for the rock to travel in a circulat path, in a vertical plane. What mathematical condition must the centripetal acceleration of the rock satisfy for the string to remain taut when the...

Homework Statement A sample is put in tension and a strain rosette gives the following results: i) Calculate principal strains and poissons ratio using Mohrs strain circle. ii) Calculate principal stresses from principal strains and poissons ratio. Homework Equations Mohr's strain circle γ =...

Homework Statement The line "4x + 3y -4=0 " divides the circumference of circle centred at (5,3) in ratio 1:2.whats the equation of the circle Homework Equations 2πr Distance of a line from point Radius of general circle The Attempt at a Solution I tried finding the distance of the centre...

Homework Statement A particle is moving clockwise in a circle of radius 2.50m at a given instant of time. I have to find radiant and tangential acceleration and the speed of the particle. The acceleration vector is 15.0 m/s² and the angle between the radius and the acceleration vector is 30°...

Homework Statement For the equation y=cx[L−x] say for a circle with the value of L at 100 meters and the value of x at 25 meters. What would be the value of the constant c for a perfect circle. 3. Attempt at the Solution: I can approximate and graph this with different values of c however I'm...

Homework Statement "Find the center and radius of the circle that passes through A(1,1) and is tangent to the line y=2x-3 at the point B(3,3). (Picture of the graph: https://imgur.com/a/0wAnqcU) Homework Equations Here's a link: https://imgur.com/a/y71Z9GY The Attempt at a Solution Soo, I've...

I have 3 point on a perimeter of circle. How I prove/show between every the two point of them there is always short way that the way between the other points?

. Homework Statement Let imagine you have gras field formed as a semi circle and you want to fence in that area. The fence is connected to a wall, so you only have to fence in the area formed by the semi-circle. You have to use 60 meters of fence bought at a hardware store. Homework...

When a merry go rounds tangential velocity approach c, and horses look closer than when at rest, what is reduced, angular velocity or radius?

Homework Statement The half thin steel plate has a radius of 4 meters and a surface density of (3+r) kg/m^2, where r is the radial distance from the origin. Using calculus, find: A. its area B. its mass C. Its center of mass with respect to the origin shown, D. It's rotational inertia about the...

Homework Statement Homework EquationsThe Attempt at a Solution This problem belongs to the topic "calculus of variation ". The fundamental problem of “calculus of variation” is to find a function y(x) such that the integral ## I = \int_{x_i }^{ x_f} \phi (y’, y, x) ~d x ## is extremum...

The basic concept is to have your space probe(s) - likely nanocraft [1] on a spinning object in space which allows you to preserve the momentum you give it while accelerating it faster. Then once you are at a speed you can simply release the nanocraft in the direction you want it to go in. More...

Known data: In the picture, CD = 10 cm. What is the area of shaded area? Equation: I know, Area of a circle = ##πr^2## Diameter of a circle = ##2πr## Attempt: Here, ## r = 10/2 = 5 ## So, diameter ## = 2πr = 2*3.1416*5 = 31.42 cm ## And area of the circle ## = πr^2 = 3.1416*5^2 = 78.54 cm^2...

In deciding which shape of ring I should use to secure an anchor to an anchor trolley I came across two choices, a circular ring or a triangular ring. While either will surely work, I began to wonder which would be more difficult to pull apart. Most of the information I found is about forces...

I have no idea what to do please help me. although i did this for the second equation, x/2h+y/2k=1 this represents an elipse first equation is circle

Let us say we form a circle with stick, just like a sundial. But instead of one stick in the center, we put sticks all around on the circle. Will the shadows all point in the same direction?

Generally in a circle, the radius of the circle is uniform around the circle due to it being at the center, this is the obvious part. However, let's say the the radius was shifted away from the center so that it is somewhere in the circle, in this case called r'. Given that the original radius...

Homework Statement Homework Equations f=ma v^2/r The Attempt at a Solution Σfx = FNcos(θ) = (v^2/r)*m Σfy = FNsin(θ) - mg = 0 FN = mg/sin(θ) (mg/sin(θ))*cos(θ) = (v^2/r)*m gcos(θ)*r = v^2*sin(θ) r = v^2sin(θ)/gcos(θ) v = 150m/s θ = 38 r = 1793m i have...

π is defined by the ratio of the circumference (R) of a circle to its diameter. The area of the circle is πR². Can this be derived without calculus (or Archimedes method)?

If the line x + my = 1 is a tangent of the circle $$x^2+y^2-4x+6y+8=0$$, the value of m is ... A. -2 B. $$\frac{1}{4}$$ C. $$\frac{1}{4}$$ D. 3 E. 4 Looking at the circle's equation, the center is (2, -3) and the radius is $$\sqrt5$$. If I know the coordinate where the line meet the circle I...

Homework Statement [/B] problem - https://imgur.com/SKeTUXNHomework Equations Mohrs circle The Attempt at a Solution [/B] I have drawn 2 induced loading elements (shown at the bottom of of my working) I just seem to have conflicting information from some class examples and am wondering...

Homework Statement Mohrs circle question - https://imgur.com/SKeTUXN Shear stress in I beam question - https://imgur.com/34yTyCAHomework Equations Mohrs Circle - None Shear stress in I beam - I = d . b^3 / 12 tmax = (F / I . b) . (A1 . y1) + (A2 . y2)The Attempt at a Solution For the...

One of the tangent line equation of the circle $$x^2+y^2+6x-8y+12=0$$ at the point whose absis is -1 is ... A. 2x - 3y - 7 = 0 B. 2x - 3y + 7 = 0 C. 2x + 3y - 5 = 0 D. 2x - 3y - 5 = 0 E. 2x - 3y + 5 = 0 By substituting x = -1, I got: $$(-1)^2+y^2+6(-1)+8y+12=0$$ $$1+y^2-6+8y+12=0$$...