# Hoop kinetic energy

1. Dec 7, 2013

### 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

File size:
6.1 KB
Views:
48
2. Dec 7, 2013

### BOYLANATOR

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

3. Dec 7, 2013

### rmfw

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

4. Dec 7, 2013

### BOYLANATOR

Yeah it's right now