What is the Lagrangian for a Mouse on a Rotating Wheel?

[starryskiesx]

Homework Statement

A mouse of mass m runs around the inner circumference of a vertical wheel which is free to rotate about the centre. The wheel has mass M and moment of inertia I. Let θ be the angle that the radius vector makes to the mouse from the downward vertical at time t. Write down the lagrangian for the motion.

Homework Equations

L = T - V

The Attempt at a Solution

So I can write down the kinetic energy of the mouse quite easily, in polar coordinates it's at constant ρ so T_mouse = 1/2*m*a^2*θ^2
Also the potential energy is V=mgacosθ.
The bit I'm confused about is the rotational energy of the wheel

Thanks!

 

[tiny-tim]

hi starryskiesx!

(try using the X² button just above the Reply box )

1/2*m*a^2*θ^2

you mean 1/2*m*a²*ω²

The bit I'm confused about is the rotational energy of the wheel

1/2 Iω²