Bead on Frictionless Rotating Ring

A ring made out of frictionless wire rotates at a constant angular velocity. A bead slides freely on the ring. Find the equations of motion. Are there any equilibrium points? Which ones are stable? For those that are stable, find the frequency of small oscillations.

[@jayronyucker4272]

really good explanation for a homework problem I am stuck on in my Undergrad 3rd year Classical Mechanics course

[@reaniegane]

Thank you. You did an excellent job with explanations: clear and detailed without leaving anything out, even simple stuff, just what I needed.

[@anuragjoshi5004]

well explained

[@johnfoltz4713]

I think you may have made a minor mistake in your potential energy portion. I think the inertial force for your reference frame is actually a component of kinetic energy.

[@HilbertXVI]

Yep, it is

[@codiekev7399]

I agree.

[@dividedshark7511]

You really saved my butt, thank you!

[@shuvajitkhatua9905]

Why do you consider rotation kinetic energy as a potential kinetic energy???
Please help......

[@hadjuntame35]

your are the man! thank you!

[@Guruji-vz8eg]

If theta = pi then sin theta = 0 , why we are considering it is equal to minus theta

[@rajanmishra329]

this is under free space whats about in the gravitational field

[@kemalaziz9696]

He includes a gravitational potential.