From what I understand,
if you let
f(x) = xsinx
and u = sinx
then
f(u) = u*sin(u)
= sin(x)*sin(sin(x))
and likewise for sin(pi - x)
If you look at the proof, you see that the fourth line should be:
sin(x)*sin(sin(x)) = sin(pi - x)*sin(sin(pi - x))
which seems correct.
Thanks for the reply! That was kind of what I was thinking. But the differential cross section isn't lorentz invariant (at least I would think it isn't). So the best you could do is find some relationship between the CM frame components and the Lab frame components and dump those in. But the...
Why is it that the differential cross section for processes like Inverse Muon Decay (IMD) are always given in the CM frame? Every paper I have seen that discusses Inverse Muon Decay gives the differential cross section in CM frame. Is it very hard to calculate the differential cross section in...
Andrew Delano already made this exact fridge in 1998, check out his papers at: http://www.me.gatech.edu/energy/students/andy.htm. They should answer some of your questions.
If we are talking about a rollercoaster going around a circular loop, then I believe you have those equations backwards . In the rollercoaster case, the restraining normal force aways points radially outward and gravity always points downwards.
So it would be
N - mg at the top
N + mg at the...
For the spheres problem, they will meet. Just replace either of sphere with a point particle. Two point particles traveling head on towards each other will meet if their velocities are equal, opposite in direction and constant.
The reason I am considering point particles here is that if the...
Many things here. First displacement is a vector quantity and so is velocity. The equation,
velocity = displacement/time
is a vectpr equation, describing the AVERAGE velocity.
If you travel around the world, starting and ending at the same location, at a constant speed, your average...
IMO, You should start your study off with
John R Taylor - Classical Mechanics
This is one of the clearest undergraduate Classical Mechanics textbooks ever written. Taylor accentuates understanding over anything else. This textbook will give you a great understanding of Classical Mechanics...
Does mathematics truly have "proofs"? A proof, at least from the way I see it, is an argument using logic. But where did our system of logic come from? Observation. So mathematics, indirectly, is a by-product of the real world and thus cannot find absolute truth.
Just some thoughts, I could...
Hmmm I typed all of that out and I think that helped me figure it out.
Phi would be the same, theta would have to satisfy the law of reflection along the plane formed by the incoming ray vector and the normal vector. This is of course a general solution and would work for any object (cube...
I am writing code for a particle simulation and I have this question:
Homework Statement
A particle, with initial coordinates (xi,yi,zi) w.r.t a fixed origin in a global rectangular coordinate system, is traveling toward one of the faces of a cube with a speed whose direction can be described...
The fine structure constant is not a law, it is a constant. Changing the fundamental constants WILL change the physics.
But you asked do the laws change, and the answer, is clearly no.
The problem with saying something is finely tuned is that every measurement of every quantity is...