That is precisely the relation you need... just look at the derivation a little longer.
For the angular momentum is conserved, so you just need to calculate the angular momentum in the first case with the circular orbit. (suppose the star is fixed ...)
This is simply:
L=mR^2\omega...
you don't need Mathematica or anything, just solve the simple second order DE for z<0 and z>0 (the delta function term is zero here) and then match them at z=0. The function itself should be continuous and then there is a jump in the derivative at z=0 due to the delta function.
Your normalization factor should be :
\frac{{{Z}_{1}}\left( T,V \right)}{{\bar{N}}}=\frac{V}{{\bar{N}}}\left( \frac{2\pi m{{k}_{B}}T}{{{h}^{2}}} \right)^{3/2}
The n in the drude law is the number density. i.e. the number of electrons per unit volume. In your normalization constant what...
Suppose the charge on the inner sphere is Q. Now surround the sphere by an imaginary sphere S of radius r. By Gauss's law:
\oint_{S}\textbf{D}\;d\textbf{f}=Q
Where df is the element vector of the spherical surface. Consider a linear medium in this case the displacement field proportional...
Use the fact that the polar angle dependence of the permittivity arises only in the displacement field not the electric field, hence the electric field has only radial dependence.
To find the capacity you need to find the potential difference between the two plates. For this use the integral...
Suppose \psi_n(x,t) are the eigenstates with energy E_n.
Then a generic state (general solution of the Schrodinger equation) can be written as the superposition of these states:
\psi(x,t)=\sum_{n}a_n\psi_n(x,t)=\sum_{n}a_n\psi_n(x)e^{-iE_n t/\hbar}
Now match this with the initial...
We cannot really examine the details of the friction force since the surface is very disordered i.e. looking at it in a microscope you will see its "messed up". We can talk mainly about the net effect of the friction force...
You are mixing things up. The Quantity given on the webpage is is the "Area moment of Intertia" not the mass moment of inertia. Read on the two quantities and then you will see what to do...
Do not expand the Euler-Lagrange equations. But do a trick like this:
The Lagrangian is:
L = \frac{1}{u}\sqrt{\left(\frac{dv}{du}\right)^2-1}= \frac{1}{u}\sqrt{v'^2-1}
Now you see this doesn't depend on $v$. The Euler Lagrange equations then give:
0=\frac{\partial L}{\partial...
Try using some physical arguments. The left hand side is the solution to Laplace's equation considering azimuthal symmetry. So you can assume it is the solution with a given potential on the surface of a sphere. So the left hand side should be also a solution to Laplace's equation, but in...
Yes you can go ahead and use the conservation, there is no outer force acting on the system. The Boat is not fixed by some outer force so we can translate it in space and get the same dynamics meaning linear momentum is conserved (we assume the effect of water on the boat negligible).