Max ω of circular hoop rotating around a peg and oscillation

[Phantoful]

Homework Statement

Homework Equations

F=ma
τ = Iα = rF
v=rω, a=rα
L = Iω
Center of Mass/Moment of intertia equations

The Attempt at a Solution

[/B]
So right now I've tried to model the force acting on the ring as it goes around the peg, but I think centripetal force is involved and I'm not sure how to use that in my equations of motion. A general idea I have is that rotational velocity should be highest when the hoop's center is at it's lowest possible point.

Say the peg is the z-axis coming in/out of the page, the moment of inertia of the hoop should be in relation to that axis. By the parallel axis theorem and the fact that a ring's moment of inertia is usually MR², it would be I = MR² + MR². From this should I be using rotational energy equations or am I far off/should do something else?

For B I am completely lost but I'm pretty sure I might need to solve A first for it.

 

[BvU]

A general idea I have

Good idea. Your intiuition is good, but: on the basis of what physics considerations ?

centripetal force is involved

On the mark again ! [edit] to avoid wrongfooting you: specifics for it may not be needed for the answer..)

am I far off/should do something else

and again ! SO: no and no. Just go ahead (and post if stuck...)

For B I am completely lost but I'm pretty sure I might need to solve A first for it.

My feeling this time is different: there is no need, but solving A first is a good strategy.