1
$\begingroup$

I have some doubts about the next excercise:

A bar of length $2a$ and mass $m$ moves freely with both of its extremes on a ring of radius $\sqrt2a$. The ring can rotate freely in a certain diameter, remaining the center fix. Find the equations of motion.

I did it using the balance of angular momentum, but I want to try to do it with the Lagrangian. But I have a problem. The energy of the ring is easy to calculate (just a rotation), but the energy of the bar I am not sure how to do it. ¿Is a translation of the center of mass plus a rotation? ¿Or just translation? ¿Or just a complicated rotation?

I did this picture to illustrate:

enter image description here

Thanks!

$\endgroup$
1
  • $\begingroup$ If there is no friction then the rotation of the ring is irrelevant. $\endgroup$ – John Alexiou Feb 3 '14 at 17:55
2
$\begingroup$

There's the motion of the center of mass of the bar (translational kinetic energy) and the motion of the bar about its center of mass (rotational kinetic energy). There's also the gravitational potential energy from the bar, if applicable (you didn't specify on earth or in outer space).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.