is A fead of mass

m

is constrained to move without friction on : Faround a wertical diameter of the hioop. Une a palar angh f wal as acimuthal angle

\\\\phi

to deacribe the ponition of the beat on the liop, with

\\\\omega =\\\\phi

. Take

\\\\theta =0

at the bottom of the lisop.\ a) Set up the Lagrangian and obtain the equation of motion en ter brad.\ Find the eritical angular velocity

\\\\omega =\\\\Omega

below which the betten d the hoop provides a stable equilibrium ponition fer the bent.\ d) Fod the stable equilibrium position for

\\\\omega >\\\\Omega

.

of radius R. The hoop totates aithon withowt frictios os a as acimuthal ancle $ to describe the ponition of the bead on the hop, with =. Take =0 at the bottom of the liopes. Set up the Lagrangian and obtain the equation of mokto bead. whind the critical angular velocity = below which the brote dr the hoop provides a stable equilibrium ponition for the brut. d) Fad the stable equilibrium position for >