Lagrangian Mechanics Question: A Yoyo radius a and b

[BiGubbs]

Homework Statement

A yoyo falls straight down unwinding as it goes, assume has inner radius a, outer radius b and Inertia I. What is the generalised coordinates and the lagrangian equation of motion?

Homework Equations

L=T-U where T is kinetic energy and U is potential

The Attempt at a Solution

So i assumed that there are 2 parts of kinetic energy, downwards and rotational, the downwards:

1/2 m Y(dot)^2

and rotational

1/2 I (Theta)(dot)^2 .

Potential is simply: mgy

This gives a lagrangian of L= 1/2 m Y(dot)^2 + 1/2 I (Theta)(dot)^2 - mgy
with general co-ords theta and Y, is this correct?

 

[kuruman]

So far so good.
In which direction is your generalized coordinate y increasing? Are there any constraints to be imposed? Where is your zero of potential energy? Where is your equation of motion?