Circle Definition and 1000 Threads

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?

What is the most compact way of arranging 5 circles inside 1 large circle. If possible, show it by drawing a picture.

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?

Can anyone explain how to draw a leading edge circle of an aerofoil. Where is the center and what is the radius of the leading edge circle

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 [SIZE="4"][FONT="Arial Black"]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

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...

Homework Statement A*certain*soil*has*c’*=*12kPa*and*φ’*=*32°.*The*major*and*minor*principal*stresses*at*a*point*in*this* soil*are*348*and*160*kPa*respectively,*and*the*pore*water*pressure*at*this*point*is*96*kPa.*Draw*...

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...

Ok so there are two part to this problem: Info: A jet pilot takes his aircraft in a vertical loop Part 1: If the jet is moving at a speed of 1500 at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not...

Homework Statement We are given the unit circle and the point (5,2). There are two lines that are tangent to the unit circle and they both intersect at the point (5,2). What are the points where these lines are tangent with the unit circle. Homework Equations Tangent line of a circle at...

Homework Statement The radius of a circle is measured to be 14.3+-0.3cm. Find the circle's area and the uncertainty in the area. I don't understand how to correctly apply uncertainty equations with sigma and partial derivatives to these types of problems. Homework Equations...

Homework Statement Find the centre of the circle which passes through the points (1,-2) and (4,-3) whose centre lies on the line 3x + 4y = 7 Homework Equations The Attempt at a Solution distance from the centre of the circle to the given points is equal by distance formula and...

Homework Statement Find the equation of the circle which touches the axes and whose centre lies on the line x-2y=3 Homework Equations The Attempt at a Solution The given line passes through 1st, 3rd and 4th quadrants. So the centre of the circle may lie in any of these i.e. it...

Homework Statement A bicyclist travels in a circle of radius 22.5 m at a constant speed of 8.62 m/s. The bicycle-rider mass is 79 kg. Calculate the magnitudes of (a) the force of friction on the bicycle from the road and (b) the net force on the bicycle from the road. Homework Equations...

I'm trying to do a project that requires me construct a circle with n chords. I need to find the maximum number of regions are obtained. I believe the way to do this is to have every new chord intersect every other chord without three chords intersecting at one point. In other words: is it...

Homework Statement let f: J --> R^2 be a unit speed curve curve and define it's tangentially equidistant campanion by g(u) = f(t) + r*f'(t) for a fixed r>0. Show that the centre of the osculating circle of f at some u in J is the intersection of the line normal to f'(u) through f(u) and the...

Can somebody give me an example whereby I use the inversion with respect to a circle (unit circle or otherwise) and the problem becomes easier. I guess I am asking: how do I make use of this notion. Or a problem that involves inversion, period. Thank you

Homework Statement Someone gave me this problem: finding the radius of the circle inscribed in the triangle with the given lengths. The Attempt at a Solution The person asking about this problem said it was taken from a beginning algebra textbook. I tried figuring it out using just...

Homework Statement y^2 + 4y + z^2 = 5, x = 3 Homework Equations The Attempt at a Solution I know that the calculated coordinates must satisfy the above equation, but I don't know how to go about solving for those coordinates. The best I could do was to equate z = \sqrt{(-y + 5)(y + 1)}.

Homework Statement A ball swings in a vertical circle at the end of a rope 1.30 m long. When the ball is 36.1° past the lowest point on its way up, its total acceleration is (-22.5 i + 20.2 j) m/s2. (a) Determine the magnitude of its radial acceleration. (b) Determine the speed and velocity...

Hi Let's say that we have equation of circle as x2 + y2 = R2 and equation of ellipse in quadratic form as A x2 + B y2 + Cx + D = 0 if the circle is inside the ellipse, so there is no intersection ... Are x and y imag in this case? /or/ is one of them imag and the other is real...

I have a circle and I need to find a particular point along it. The circle has a known radius (r), center (a, b), and I know a coordinate point upon it (x1, y1), as well as an arc-length (d). From that point x1, y1, how do I find out the point x2,y2 which is arc-length d away from the point...

I thought of an interesting paradox on my way home today. Suppose you have one-dimensional, finite universe without boundary. A circle. Special relativity seems to fail on this small world. Take two objects in relative motion. As they pass by each other, they synch their clocks. Stop...

Homework Statement Show that the square, when inscribed in a circle, has the largest area of all the 4-sided polygons. Try to show that all sides of a quadrilateral of maximal area have to be of equal length. The Attempt at a Solution How do you start? I don't get how showing the sides...

Homework Statement how do you find the radius and center with x2+y2=16 of a circle graph Homework Equations The Attempt at a Solution I am completely stump don't even know where to start on this.

Homework Statement I am curious why is the equation of a quarter of a circle (y = \pm \sqrt{r^{2}-x^2}) the same as half a circle? Shouldnt they be different? Homework Equations n/a The Attempt at a Solution n/a

My friend and I were debating if there really could be a perfect circle in nature outside the human brain? What do you think? If you think there is, please back it up with evidence.

A particle of mass 100grams rests on a smooth horizontal table and is attached to one end of a string which passes through a small hole in the table and supports a particle of 200grams. With what velocity must the 100gram mass be projected on the table so as to describe on the table a circle of...

We have a circle of certain radius.How many circles of smaller radius(we are provided with the ratio of radius) can be placed within the larger circle? Help me to determine the least number of the smaller circles that can be filled?? I am trying to generate a generalized solution, and looking...

I'm trying to plot the pressure distribution around a cylinder in a uniform flow field, so that the graphic is a circle with the pressure curve around it, like in the image below. http://img843.imageshack.us/img843/4649/63792687.th.jpg Uploaded with ImageShack.us I have the equation for...