A point mass is constrained to move on a massless hoop of radius a fixed in a vertical plane that rotates about its vertical symmetry axis with constant angular speed [tex] \omega [/tex].(adsbygoogle = window.adsbygoogle || []).push({});

a. Obtain the Lagrange's equations of motion assuming that the only external forces arise from gravity.

Should I have seperate KE components for the linear velocities as well as the angular velocity? I have this so far (with seperate x,y and z velocity components written in spherical coordinates) [tex]T=\frac{m}{2} v^2 + I\omega^2[/tex]. I'm pretty sure that is correct, but I don't know what to use for the moment of inertia? Can I just use the moment of inertia for a spherical shell, or would I use that of a ring or something else entirely?

EDIT:

Since [tex]\omega[/tex] is the rate of change of the angle [tex]\theta[/tex] in spherical coordinates, could I set that equal to [tex]\frac{d}{dt}\theta[/tex] in the kinetic energy term? Or can I not ignore the moment of inertia like that?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Lagrangian Question

**Physics Forums | Science Articles, Homework Help, Discussion**