I'm applying for graduate school but am from a basically unknown state school. My stats can be found here: http://www.physicsgre.com/viewtopic.php?f=21&t=5735.
I am looking for a low ranked or unranked theoretical cosmology/hep-th school or a similarly ranked observational astronomy program...
Oh, wow that makes a lot of sense. I got in the habit of multiplying f(z_0) by whichever term was creating the singularity in the denominator because a lot of the first problems we did would have something simple like (z-1) there. So then, (z-z_0) would equal exactly what was there. Anyway...
I'm asked to evaluate the following integral: \int_{c} \frac{30z^2-23z+5}{(2z-1)^2(3z-1)}dz where c is the unit circle. This function has a simple pole at z=\frac{1}{3} and a second order pole at z=\frac{1}{2}, both of which are within my region of integration. I then went about computing the...
I'm beginning to apply to grad schools (primarily in observational or computational cosmology and extragalactic astronomy) but have a deep interest in M-theory and quantum gravity although I haven't been able to study it. I very much enjoy theory and think that I would find studying M-theory or...
You're right, the equation above would be invalid for a reference frame at rest in which both cars have some initial velocity, which is what we should be considering. I'm just trying to give you a feel for how an equation like that might change when the car at rest starts accelerating. The...
For an inelastic collision in which only one object is moving initially (let's call it object 1), the final velocity of the combined objects is given by v_2=\frac{m_1}{m_1+m_2}v_1. Now, the initial velocity v_1 is the velocity of the moving object but can also be thought of as the velocity of...
Okay, so I did that and ended up with a final angular momentum nearly exactly the same as my initial but missing that factor of three. The factor of three came from integrating a sine cubed due to having to break up the theta hat into its cartesian components. Do you know whether I should or...
Oh, so the electric field at any arbitrary point on the sphere (in terms of \theta) would be \vec{E}=\frac{a\sin\theta}{2}\frac{dB}{dt}\hat{\phi} using Faraday's law, correct? Then to find the total torque on the sphere I would have to integrate this then use \tau=\frac{dL}{dt} to solve for the...
You're right. I was using Faraday's law, my mistake.
For a sphere of radius a, at any polar angle \theta, the radius of the loop around the sphere is R=a\sin\theta, thus the path integral of that loop is simply E2\pi a\sin\theta since we know E is in the same direction as the path at all times...
Hm. So, an integral with respect to the polar angle theta? If I consider a sphere whose radius is a<r<b, the radius of each thin annular ring is then R=r\sin\theta? But how do I set this integral up with Ampere's law?
Good point. I'm not really sure. I suppose I just choose an arbitrary loop that is centered on the z-axis? That's basically my question. I'm not sure how to approach this part.