It's actually -2\pi, not 2\pi where the log of 1 is defined. That is what is throwing me. I'm trying to get a clear picture in my head instead of just a plug and chug with the single-valued (analytic) definition of the log in complex, which works but doesn't lead me to using or understanding...
Homework Statement
Consider a branch of \log{z} analytic in the domain created with the branch cut x=−y, x≥0. If, for this branch, \log{1}=-2\pi i, find the following.
\log{(\sqrt{3}+i)}
Homework Equations
\log{z} = \ln{r} + i(\theta + 2k\pi)
The Attempt at a Solution
This one...
Thank you, LCKurtz.
I edited my post right as you were replying, I guess. I found and added the formulas and added the m = to the front of the equation for mass along the line integral.
So, if we're using \rho = x^2 + y^2 + z^2 we get \rho = t^2 + \cos^2{t} + \sin^2{t} which is just \rho...
Homework Statement
Find the mass and center of mass of a wire in the shape of the helix x=t, y=\cos{t}, z = \sin{t}, 0 \le t \le 2 \pi, if the density at any point is equal to the square of the distance from the origin.
Homework Equations
Arc length formula:
ds =...
Thank you for your reply, AlephZero. It's interesting to consider the edge case of points that happen to also be collinear. I'll keep that in mind in case anyone throws that one at me as a curveball. :)
Thank you for your reply, Hyperbolful. You are correct, the question was involving given specific points. It wasn't intended to be a formal proof, just an exercise.
I recently solved a problem involving multiple points that were intended to be proven to be coplanar. Someone else suggested to me that I should be using the much messier scalar triple product.
However, I worked the problem in a different way. I treated it like a conjecture (I assumed that...
I decided to submit my answer and determined that I was correct. The problem appeared to be more complicated than it was (because it's helical).
The reason I mentioned it was the algebra based physics course is that they don't do matrix mathematics to determine anything in the algebra based...
I never learned how to do this since I'm taking an algebra based physics course instead of the calculus based one (I wish I'd thought more about that, but C'est la vie).
I know how to do the actual calculations using matrices, but I don't know how to represent a problem like this in matrix...
I'm not sure I understand what you mean. The direction of the magnetic field is upward. That tells me that the only path along which the particle will feel a force is along the x axis, which is perpendicular to it. I am not assuming that there's any acceleration upward, but that the velocity...
Homework Statement
At t=0, a proton is moving with a speed of 5.8\times 10^5 m/s at an angle of 30° from the x-axis, as shown in the figure. A magnetic field of magnitude 1.7 T is pointing in the positive y-direction.
What will be the y-coordinate of the proton 15 \mu s later?
Homework...