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    Why Vectors product the way it is?

    I have come to this thread rather late, however I'd like to make a few comments. Vector analysis was worked out in the early 1880s by the American mathematical physicist, J. Willard Gibbs. In the period 1881-1884, he circulated a pamphlet he had written to interested people and in 1901 Yale...
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    An Easy Metric for Einstein Field Equations

    One of the easiest metrics to begin with is the spherically symmetric metric that leads to the Schwarzschild solution. Another relatively easy metric, but not quite as easy algebraically is the axi-symmetric metric that leads to the Weyl solution. As the previous post indicates, using computer...
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    Covariant derivative in spherical coordinate

    Isn't there a problem with the indices here, or am I missing something? Three k's and 3 i's in each term doesn't ring true to me.
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    Important and/or Interesting Spacetimes

    George, In your first post you mentioned the "Schwarzschild Constant Density Spherical Solution". Is this an "interior" solution? Could you cite a reference for it? Are there any interesting solutions interior to a spherical distribution of "dust" --this could not be static and would have to...
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    Frame dragging around a rotating black hole.

    Thank you, Steve and George.
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    Frame dragging around a rotating black hole.

    Thanks to all for the references on frame dragging. I have another question. Consider the very massive black holes believed to be at the center of most spiral galaxies. If they were rotating rapidly would the frame dragging effect alter the orbital dynamics of stars in orbit around the black hole?
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    Frame dragging around a rotating black hole.

    Stevebd1, do you have a good reference for the derivation of the equations that describe frame dragging? Is this the same as the Lense-Thirring effect?
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    Need help with Physics Vectors, not sure how to do them

    Here's how it works in detail: Each path that the girls takes can be represented by a vector. When drawn out in an x-y coordinate system you can express each vector in terms of its x and y components. The resultant vector is found by adding up all of the x components and then adding up all the y...
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    Need help with Physics Vectors, not sure how to do them

    That is the correct approach. The resulting displacement is just the sum of those individual vectors. If you drew them to scale, you can connect the starting point to the ending point and measure that vector to get your answer.
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    Circular motion velocity

    Here are a couple of hints: (1) The time frame for the velocity and the acceleration is the same: 5 sec. (2) Find the distance that the tip of the second hand travels in 5 sec. You can do this by knowing that it travels 360 degrees, or 2 Pi radians in 60 seconds. From that tells you can figure...
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    Electric potential on circle problem

    Yes, you calculate each potential separately and then add them all up. For the curved pieces construct an integral for a potential dV from a bit of charge dq. then integrate. Your limits of integration depend on how you choose to draw your diagram, but the total angle is the same no matter how...
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    True or False(Help)

    Several of your answers above are wrong. Why don't you check the following terms on Wikipedia: Refraction Diffraction Dispersion Finally, in an old film style camera the image is made by a chemical reaction. What is the difference between a real and a virtual image? Which one can induce...
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    Work against an electric field due to a point charge

    Besides the approach that I mentioned in my previous post, you can also use the fact that Work = qV where q is the charge that's being moved, and V is the change in electric potential. What you calculated in your work below, was the change in electric potential, not the work. All you have to...
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    Work against an electric field due to a point charge

    Also, I should mention that you are correct. Work is done only when the charged is moved along a radial path.
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    Work against an electric field due to a point charge

    In brief, Work = Force times distance. So your equation for work should be W_{\vec{E}} = -\int_{r_{1}}^{r_{2}} q \vec{E}\cdot d\vec{r} Where the force is qE, q being the charge that's moved, and E is the field due to the charge Q.
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    Work against an electric field due to a point charge

    Your idea is correct, but your first equation is wrong. Usually gravity is ignored because the gravitational force is small compared to the electric force.
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    Thermodynamics, Dilation.

    I would make the approximation that the expansion of the glass can be ignored. Then you don't have to worry about the expansion of the cross section and the linear formula will give you an acceptable answer.
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    Linear Momentum - Person on a Plank on a frictionless surface

    Okay, draw a picture of the girl on the plank. Label the girl's center of mass. Label the plank's center of mass. Look up how to calculate the center of mass of the girl + plank. That point doesn't move. However, the girls and the plank DO move. They have to move so that in their final position...
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    Thermodynamics, Dilation.

    Here's a couple of things you might want to consider. (1) What is the temperature of the mixture at the triple point? (2) What is the pressure at the triple point? (3) What is the pressure at the normal freezing point of water? What does that imply about the difference between the triple point...
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    Linear Momentum - Person on a Plank on a frictionless surface

    The essence of this problem is that since all forces involved are internal to the system, the center of mass of the system (plank plus girl) does not move even though the girl and the plank do move. The velocity of the girl or the plank is immaterial, {though as a practical matter, she should...
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    Centripital Force? Help

    Here's some hints: The frequency is the number of revolutions per second (or fractions of a revolution per second). That depends on the velocity of the mass because the faster it goes the more complete revolutions it can make in a given time period. But you have this nice little equation that...
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    Geodesic equation in new coordinates question

    Sorry it took a while to get back to you. If you have it available, look at page 102 of Weinberg's "Gravitation and Cosmology. There he shows that the geodesic equation transforms like a vector.
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    Checking whether my Diff EQ limit problem is correct

    I think you wrote the wrong thing. Don't you want to take the limit as t goes to infinity?
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    Correspondence betw. Hamilton-Jacobi & Schrödinger eqns.

    Here is the reference that I said I would post: "Quantum Dynamics with Trajectories" by Robert E. Wyatt, published by Springer.
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    Correspondence betw. Hamilton-Jacobi & Schrödinger eqns.

    You might be interested in Section 4.2 of "Introduction to Quantum Mechanics: A Time Dependent Approach" by David J. Tannor on Bohmian mechanics and the classical limit. If you use Squeezed's suggestion and substitute \psi= A(\textbf{r},t) e^{\frac{i}{\hbar}S(\textbf{r},t)} then the...
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    Puck momentum

    The components of the momentum in the x and y directions are separately conserved. Which component of the system's momentum is zero before the collision? Whenyou figure this out, you will be able to answer your question.
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    Does an electron moving along a geodesic radiate?

    I'm interested in the references. Please post a couple of them.
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    Tensor algabra, dummy indices manipulation

    The thing to realize about dummy indices is that they have no intrinsic meaning except that they are to be summed over. Thus, in the product z_{abc}x^a x^b x^c you can replace a with d and the meaning is the same. You might want to systematically replace each of your given letters with...
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    Exact length of the curve analytically

    Let me first fix your expression by putting in the "tex" commands: That doesn't look right. Now, y = (9 - x^{\frac{2}{3}})^{\frac{3}{2}} has a derivative that looks like \frac{dy}{dx} = -(9 - x^{\frac{2}{3}})^{\frac{1}{2}} x^{-\frac{1}{3}} Now when you square that mess so...