Coordinate Definition and 910 Threads

Homework Statement A cubical box has been constructed from uniform metal plate of negligible thickness. The box is open at the top and has edge length L = 97 cm. Find (a) the x coordinate, (b) the y coordinate, and (c) the z coordinate of the center of mass of the box. Homework Equations...

Homework Statement Everyone tells me that I should use right-handed coordinate systems. But no one tells me what happens if I don't. What is the danger of not using right-handed coordinate systems?Homework Equations The Attempt at a Solution

Hi, I am using the book "Advanced Engineering Mathematics" by Erwin Kreyszig where I am reading on the transformation of coordinates - when changing from \int f(x,y) to \int f(v(x,y),v(x,y) it is necessary to multiply with the size of the jacobian, |J| - I cannot find the proof in the book...

Homework Statement Transform the following vector into cylindrical coordinates and then evaluate them at the indicated points: \vec A = (x + y)\hat x at P_1 (1, 2, 3) Homework Equations r = \sqrt{x^2 + y^2} \phi = \tan^{-1}(\frac{y}{x}) z = z The Attempt at a...

Homework Statement Can someone give me a real rigorous definition of what a right-handed coordinate system is? I can't find one on the internet. Is this true: A coordinate system is right-handed IF AND ONLY IF x-hat cross y-hat = z-hat ? Homework Equations The Attempt at a...

Homework Statement Describe in words the region of R^3 represented by the equation or inequality. Homework Equations xyz=0 The Attempt at a Solution I'm not really sure how to look at the equation. I would think its just the point (0,0,0). Can someone explain if this is wrong.

is one -one correspondence must for a theory like coordinate geometry , polar coordinate ,vector analysis etc to work , i.e theories which work by representing a quantity by a different set of quantities behaving alike

Homework Statement A cone rolls on a flat surface. The instantaneous axis of rotation lies parallel to the point where the cone touches the surface and the angular velocity OMEGA. The motion of the center of mass (Vcm) plus a rotation OMEGAcm about the center if mass. Describe this motion by...

I have problem with getting normal coordinates offset. I have cube1 and cube2. cube1 position is 10,10,10 and cube2 position is 10,9,10. Cube 2 offset refers to local coordinate system of cube1. If rotation of cube1 is 0,0,0 i get position offset 0,-1,0. But if cube1 rotation is 45,0,0 i get...

Help neede in coordinate geometry! Homework Statement here is the question : If the pairs of lines x^2-2pxy-y^2 and x^2-2qxy-y^2 are such that each pair bisects the angle between the other pair , then pq equals ...??the answer somehow is -1. i think it uses the concept of homogenisation (if u...

Homework Statement I want to show that the homomorphism phi:A(X)->k+k given by taking f(x_1,...,x_n)-> (f(P_1),f(P_2)) is surjective. That is, given any (a,b) in k^2 (with addition and multiplication componentwise) I want to find a polynomial that has the property that f(P_1)=a and f(P_2)=b...

Homework Statement Frame S' has an x component of velocity u relative to the frame S and at t=t'=0 the two frames coincide. A light pulse with a spherical wave front at the origin of S' at t'=0. Its distance x' from the origin after a time t' is given by x'^2=(c^2)(t'^2). Transform this...

Homework Statement In cylindrical coordinates write a function which describes the surface of the dome (brunelleshci's dome) whose center is not on the central axis but rather one-fifth of the way from the edge. the sides form a shape called quinto acuto, span of base of dome is 143 find...

(a) A point is observed to have velocity v_A relative to coordinate system A . What is its velocity to coordinate system B which is displaced from system A by distance R ? ( R can change in time) I think its v_B = v_A - \frac{dR}{dt} . But I am not completely sure why this is the...

http://p14.freep.cn/p.aspx?u=v20_p14_p_0711201047589252_0.jpg Formula: http://freep.cn/p.aspx?u=v20__p_0711201059233972_0.jpg 1)I need to find out V(\theta). But I remember that r\theta<dot> = \omega = V(\theta) Something seems like contradict Where my concept wrong? How should I...

Identify the curve by finding a Cartesian equation for the curve. r=2 My attempt: r=2 makes a circle with a radius of 2, so: \begin{array}{l} x^2 + y^2 = r^2 \\ y^2 = r^2 - x^2 \\ \\ y = \pm \sqrt {r^2 - x^2 } \\ \\ y = \pm \sqrt {2^2 - x^2 } \\ \\ y...

Homework Statement Three odd-shaped blocks of chocolate have the following masses and center-of-mass coordinates: (1) 0.310 kg, ( 0.200 m, 0.310 m); (2) 0.410 kg, ( 0.110 m, -0.380 m); (3) 0.200 kg, ( -0.280 m, 0.610 m). Find the x coordinate of the center of mass of the system of three...

Homework Statement I have 3 known point, with coordinate P1-(X1, Y1, Z1), P2-(X2, Y2, Z2), P3-(X3, Y3, Z3). straight line is draw from P1 to P2, P2 to P3. they are "not" collinear. I would like to fit a round fillet to the conner with a "Known" radius of R, and I would like to know...

I am trying to understand the derivation of the divergence formula in cylindrical coordinates. www.csupomona.edu/~ajm/materials/delcyl.pdf paper does a good job of explaining it but I don't understand 2 things that the author does. \frac{\partial\hat{\rho}}{\partial\phi} = \hat{\phi} and...

If we want to transform vector A from cooedinate ei to ei', then this formula occur: Aj' = aij Ai But I have a question, if I have found all components of Aj', then I want to transform it back to Ai, what should I do? I have tried Ai = aij Aj' but it won't give me the same number. Thanks...

Can anyone explain me what is the difference between inertial system and coordinate system in relativity? Please make me understand.

Homework Statement Describe in words the region of R3 (3 dimension) represented by the following inequality. 1)xyz=0 Homework Equations none i know of The Attempt at a Solution no idea where to start. I know that this means one variable must be equal to 0, but i don't...

Homework Statement find the transformation that turns this metric: ds^2=-X^2dT^2+dX^2 into the minkowski metric: diag(-1,1). The Attempt at a Solution attempt 1: I transformed the above metric into the coordinates that use the lines that define the light cone as the axes. Namely, u=T+ln(X)...

Homework Statement Given that Z is a complex number with condition |Z-1|+|Z+1|=7 Illustrate Z on Argand Diagram and write out the equation of Locuz Z I attempted to figured out the equation of locus Z, |Z-1|+|Z+1|=7 |x+yi-1|+|x+yi+1|=7 \sqrt{}[(x-1)^2+y^2] + \sqrt{}[(x+1)^2 + y^2] =...

4 charts seem to cover it. BUt only 2 will do for a minimal number? Just like 2 charts will do to cover a sphere? Even though there are 6 all together.

Hi everyone, wondering if anyone can help me with this little problem... An object with mass m1 , resting on a frictionless horizontal table, is connected to a cable that passes over a pulley and then is fastened to a hanging object with mass m2. Find the acceleration of each object and the...

Question Statement The straight line y=mx -2 intersects the curve y^2=4x at the two points P(x1,y1) and Q(x2,y2). Show that 1) m>-1/2, m not equal to 0. 2) x1 + x2 = 4(m+1)/m^2 3) y1 + y2 = 4/m If the point O is the origin and the point T is a point such that OPTQ is a parallelogram, show...

Basically I want to find the new limits w,x,y,z when we make the valid transformation \int^{\infty}_0 \int^{\infty}_0 f(t_1,t_2) dt_1 dt_2 = \int^w_x \int^y_z f(st, s(1-t)) s dt ds I've tried putting in arbitrary functions f, and so getting 4 equations constraining the limits, but I end up...

I know there is: A gravitational length contraction by the factor of \sqrt{1-2GM/rc^2} A time slowing by the factor of \sqrt{1-2GM/rc^2} I would have thought the former and latter affect the notions of wavelength and frequency of light respectively, am I not right? However, then...

Homework Statement Given variables in one coordinate system, give the notation used to refer to the variables in another system. The known variable is x Homework Equations The transformation is an arbitrary one. My question has to do with notation and not mathematical procedures...

I was wondering about this, I've never seen any general theorem. Obviously it takes more than one, but I would think that in general it can take quite a few, for I can't see how to cover a torus with only 2. Is there any sort of general result on this?

Homework Statement Let L be the line y=7, x=7z. If we rotate L about the x-axis, we get a surface whose equation is Ax^2 + By^2 +Cz^2=1 What are the values of A, B, and C? Homework Equations Listed above. The Attempt at a Solution Since y=7, my first point that I plugged into...

Hello everyone, I was wondering where I could get complete ecliptic longitude/latitude data over the course of as many years as possible of the Sun and Moon. Of course, by definition the ecliptic latitude of the Sun would be zero. The equatorial coordinates would be fine. Thank you for...

Hey all, According to my physics textbook, if the potential energy of a particle is a homogeneous function of the spatial coordinate r, one can transform r by some factor a and t by some factor b=a^(1-.5k) such that the Lagrangian of the particle is multiplied by a^k. I understand all of this...

What is the difference, if any, between frame fields and coordinate bases?

I know basic 2D coordinate geometry/conic sections and some vectors and calculus. What I am trying to find out is, if you rotate a conic about its axis by an angle of pi, you should get a surface in 3D. How would you go about rotating this though?

Homework Statement A rigid body consists of three uniform rods each of mass, and length 2a, held mutually perpendicular at their midpoints (choose and axis along the rods). a) Find the angular momentum and kinetic energy of the body if it rotates with angular velocity w about an axis...

How would you go about converting from a Cartesian coordinate plane to one where (0,0) is in the top left hand corner?

Homework Statement 1. Obtain an expression for operator of coordinate in momentum representation. To this end begin with definition of the average coordinate x = ∫ψ*(x)xψ(x)dx express the wave functions as wave packets in terms of plane waves, and rewrite the expression for average...

The points Q moves such that the length of the tangent from Q to the circle x^2+y^2+4x+8y+9=0 is equal to the distance of Q from the origin ). Determine the locus of Q. I am basically clueless about this question...but I will try to provide as many work I have done on this question. I assume...

How can I identify the coordinate transformation that turns ds^2 = \left(1+\frac{\epsilon}{1+c^2t^2}\right)^2c^2dt^2 - \left(\frac{\epsilon}{1+x^2}\right)^2x^2 - \left(\frac{\epsilon}{1+y^2}\right)^2y^2 - \left(\frac{\epsilon}{1+z^2}\right)^2z^2 into the Minkowski metric ds^2 = c^2dt^2...

I am a little confused with this. I know what a dative bond is, but the problem is when it comes to complex ions I do not understand. ok now for example NH_3 + H^+ = NH_4^+ So in this the lone pair of NH3 will fill the s- subshell of H and make it stable, but say in Cu^2^+ when this attracts...

Homework Statement For a universe with k=0 and in which (a/a_0) = (t/t_0)^n where n<1, show that the coordinate distance of an object seen at redshift z is r=\frac{ct_0}{(1-n)a_0}[1-(1+z)^{1-1/n}].2. The attempt at a solution I have used r=f(r)=\int_{t}^{t_0}...

The points P(cp,c/p) and Q(cq,c/q) lie on the rectangular hyperbola xy=c^2. Show that the equation of the chord PQ is pqy+x=c(p=q), and deduce the equation of the tangent at the point P. I can do the proving. And I can find the tangent as well if the word "deduce" is not there. How can you...

Given a state |psi> and an operator A with (non-degenerate) eigenstates |ai> corresponding to real eigenvalues ai, express the wavefunction psi(x) corresponding to the state |psi> in terms of |psi> Now this was a question in last year's exam that my lecturer went through, but his answer on...

I know this might be a stupid question, but I wan't to know if any of you know of any sites that convert between RA and dec coordinates to altitude and azimuth coordinates. I mean I found this site: http://home.att.net/~srschmitt/script_celestial2horizon.html But unfortunately you can't...

Homework Statement Sketch the curves with the following equations: a) y=5x^(3/4) b) y=-2x^(-3/2) Homework Equations The general equation of curves (circles, parabola, ellipse, hyperbola) The Attempt at a Solution It seems to me that this question is not exactly a coordinate geometry...

Hi, I have a pretty in depth understanding of special relativity. Recently I have been searching for mathematical proof of the Lorenz transformation. I found some information about it, but to tell the truth I didn't understand much of it. Maybe one of you guys can shed some light on the proof...

coordinate help please :) Hi i just got my home work but don't know where to start. Any help on this just to get me started would be great:) I want to make sure I am doing it right Thank you Work out the coordinates where this line meets this plane. Line x = -4 t + 4, y = -4 t + 6...

I am trying to get from one 2D coordinate system to another 2D coordinate system. I found 2 corresponding points and each system. I did the following: [a1 a2 ] * [ x1,y1 ] = [u1,v1] [a3 a4] [ x2,y2] [u2,v2] or A*x = u if I use MATLAB to...