Is Angular Momentum Conserved in a Central and Gravitational Force System?

  • Thread starter Thread starter moonman
  • Start date Start date
  • Tags Tags
    Lagrangians
moonman
Messages
21
Reaction score
0
I have a problem with a particle experiencing a central force towards some origin, as well as a gravitational force downwards. I've calculated the Lagrangian, and the equations of motion. Now I'm being asked to see if the system follows conservation of angular momentum. How do I do this? I know it has something to do with seeing if the system is invariant of rotation, but how do I check for that?
 
Physics news on Phys.org
If \frac{\partial L}{\partial q} =0 then the conjugate momentum \frac{\partial L}{\partial \dot{q}} is a conserved quantity.

If that doesn't clear things up, then post what you have for the Lagrangian.
 
But the conjugate momentum is the same as the angular momentum only in some cases.
Compute H and chech if H commutes with J.
 

Thread 'Please tell me where I am going wrong in this integral'

##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
View full post »

Thread 'Direction of the magnetic field of an oscillating charge'

Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
View full post »

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
View full post »

Similar threads

Consider the hypothetical decay of the Φ(1020) meson into 3 pions
Replies
4
Views
2K
Lagrangian with angular velocity not constant
Replies
18
Views
2K
Using Noether's Theorem to get conserved quantities
Replies
2
Views
2K
Without Lagrangian, show that angular momentum is conserved
Replies
1
Views
1K
Energy-momentum tensor for a relativistic system of particles
Replies
1
Views
1K
Action variables in a non inertial system
Replies
10
Views
1K
Lagrangian for relativistic angular momentum
Replies
1
Views
2K
Conservation of the Laplace-Runge-Lenz vector in a Central Field
Replies
3
Views
2K
Merry Go Round conservation of angular momentum
Replies
3
Views
2K
Computing the spectrum of a Lagrangian in field theory
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top