A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the centre is called the radius. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted.
Specifically, a circle is a simple closed curve that divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a disc.
A circle may also be defined as a special kind of ellipse in which the two foci are coincident and the eccentricity is 0, or the two-dimensional shape enclosing the most area per unit perimeter squared, using calculus of variations.
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...
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
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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...
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...
Homework Statement
One-hundred punctual charges equal 3uC (so Q1=3(micro)C ,Q2=3uC... Q100=3uC stand on a circle with radius r=120cm and they are equable .Find the electric field in the center of the circle and the potential in the center of the circle potencialin . How will potential...
Homework Statement
You're given a hoop with mass m and radius R balanced on top of a knife blade. (The diagram looks like a triangle with a circle balanced on the tip.) Find the period of small oscillations.
(Yes, that is all the problem says.)
Homework Equations
Moment of inertia of a...
I have a uniform rod laying on a table. A ball comes in and hits the rod making it move backwards but also rotating. Assuming that we are in a frictionless environment, how do describe the circle made by the rod?
Homework Statement
Write an equation for the circle centered on the y-axis and is tangent to a vertical line at the point (3,7)
Homework Equations
The Attempt at a Solution
(x^2)/9 + (y-7)/9
Homework Statement
A particle is moving in a circle. If the radius of the circle is doubled and the angular speed remains the same, then the angular momentum of the particle about the center of the circle will also be doubled.
The Attempt at a Solution
Im thinking it's false...
Homework Statement
Shaft diameter: 0.2m, Torque: 150 KNm, Axial Thrust(compressive): 520KN
Trying to find the angle between maximum principal stress and shaft axis and then to draw the mohr's circle to confirm this results
Homework Equations
The Attempt at a Solution
I...
Assume you're given a circle with the line AB containing its center O, such that A and B are on the circle (OA=OB=radius). A tangent t is drawn on the point A, and
I should calculate the mapping of certain points (a,b,c,d...) of the circle to the points on the tangent (at, bt, ct, dt, ...) such...
Homework Statement
Sketch the element for the stress state indicated and then draw Mohr's circle.
Given: Uniaxial compression, i.e. \sigma_{x} = -p MPa
The attempt at a solution
Below I have the sketch and a partially complete Mohr's circle...
I am having a real tough time memorizing the unit circle and it's values. What would you suggest to make easier for me to remember the quadrants, square roots, and radians?
hello
there
hi everybody
just i have been taken my final exam for calculus one CALCULUS I
there was one qeustion which i was confouse while i was reading it
Set up the intgeral area of unit circle?
I realize this is a classic problem, but I'm not sure exactly how to start on it:
Show that the closed unit square region is homeomorphic to the closed unit disc.
Problem: Given a circle of radius 1. Take a sector of this circle with internal angle A, where 0=<A=<pi/2. Find a formula for the radius of the smallest circle that will perfectly fit this sector, as a function of A.
Solution.
I used laws of sine and cosine and came up with...
How would I work out the pitch circle and number of teeth required to move the mechanism a certain amplitude? Looked over 4-5 sources for pitch circle, but cannot make sense of it..
How many rational points can be there on a circle which has an irrational centre?
(rational point is a point which have both x,y as rational numbers)
how to proceed??
answer is: atmost 2
Homework Statement
It's a problem on Halliday's Fundamentals of Physics's 24th chapter.
This problem gives us N-electrons on a circle with radius R.
The electrons are placed on the same distances so these electron positioning has a
circular symmetry.
And it also gives us another...
In a 3-D stress problem when we draw the 1st & 2nd & 3rd mohr circle for each plane what is a case or situation in which the 3rd mohr circle is smaller than the 1st & 2nd ones?
Homework Statement
An amusement park roller-coaster of
height h has a loop-the-loop of radius R. A
frictionless car starts at the top. Find its speed
at each of the points a, b, c. Find the normal
force (vector) exerted on it at points a and b.
Find the minimal h-to-R ratio that will...
Hi everyone
Consider a 2x2 partitioned matrix as follow:
A = [ B1 B2 ; B3 B4 ]
I'm sure that all eigenvalues of A are on the unit circle (i.e., abs
(all eig) = 1 ). but, I don't know how to prove it. Is there any
theorem?
Homework Statement
A bicycle is racing around on a horizontal surface in a circle of radius 19 m. The force exerted by the road on the bicycle makes an angle of 23 degrees with the vertical. What is its speed?
Homework Equations
I believe this is a uniform circular motion problem, so...
I have already drawn the circle and am happy and confident with it, but the question asks me to determine if failure has occurred and I am unsure of how to tell, I guess I don't know how to read the circle and interpret what it means.
Can anyone describe to me how you tell if failure has...
Homework Statement
For a > 0, prove that the circle x2 + y2 =1 and the parabola y=ax2 - b
intersect at four distinct points, provided a>b>1.
2. The attempt at a solution
This is the solution given in my book.
Since a>0, by figure -b<-1 i.e. b>1
also when y=0
x2=b/a (from the equation...
ABC inscribed within a circle whose diameter AC forms one of the sides of hte triangle. If Arc BC on the circle subtends an angle of 40 ddegrees, find the measure of angle BCA within the triangle
Homework Statement
Show that the line 2x+3y=27 is a tangent to the circle with centre (4,2) and radius sqrt of 13. Find the co-ordinates of the point of contact. (Without a calculator)
Homework Equations
The Attempt at a Solution
I have worked out that the equation of the circle...
Homework Statement
A softball pitcher rotates a 0.236 kg ball
around a vertical circular path of radius
0.633 m before releasing it. The pitcher exerts
a 30 N force directed parallel to the motion
of the ball around the complete circular path.
The speed of the ball at the top of the...
ALright, just a quick question concerning this diagram. Since the 90 degree angle is directed along the middle ove the circle, does that mean if you draw a line from where the circle is touching the ninety degree angle to the centre of the circle, it would make a 45 degree angle with the...
ABCD is a cyclic quadrilateral. The diagonals AC and BD intersect at right angles at E. M is the midpoint of CD. ME produced meets AB at N.
Show that ME = MC
Homework Statement
The area in the region inside the unit circle and above the graph of f(x) = x^5
Homework Equations
I don't know how to type the equation in here but the area is the integral between two integration points of the higher curve minus the lower curve.
The Attempt at a...