Kinetic Energy of a Rotating Hoop - Physics Forum

[rmfw]

Hey PF, this is just a quick question:

If there's a hoop of mass M and radius a rotating around its vertical axis (see pic) and I want to write the kinetic energy for the Lagrangian is it just $T = \frac{1}{2} M a^2 w^2$ ? Considering w the angular velocity

 

[BOYLANATOR]

Not quite. What is the moment of inertia for this set up?

 

[rmfw]

$T =\frac{1}{2} w^2 \frac{1}{2} M a^2$ ? is it more close to the answer now?

 

[BOYLANATOR]

Yeah it's right now