A bead slides on a frictionless hoop. The hoop is spinning at rate w on vertical axis. Find Lagrangian. See attached file for full problem description.
Please see the attached file.
bf Bead on Hoop rm
The system is one-dimensional since the position of the bead at any time is fully determined
by one coordinate which can be taken to be the bf angle rm $alpha$ between the direction
from the hoop center to the bead and the bf negative rm direction of the z-axis.
That is the coordinates of the bead at any time are
x(t) &= ...
The solution solves for the lagrangian for a bead sliding along a frictionless hoop.