Lagrangian of system with circle and cube

[Oomph!]

Hello. I have some problems with making Lagrangian. I need your advice.

1. Homework Statement

I have this situation:

Consider the circular path is intangible and without friction. I have to find Lagrangian for coordinates x and θ.

Homework Equations

[/B]
L = U - V

The Attempt at a Solution

I know the result from a book:

The origin of the coordinate system is at the center of the initial position of the circular trajectory.

I understand that the fist part is kinetic energy of big cube of mass M in coordinate x.The second part is kinetic energy of bead of mass m in a circle in coordinate x.
I don't understand to third part. I think that the m (mass of bead) is missing there. If I will consider that m is there, it is kinetic energy of bead in coordinate θ.
What is the poind of fourth part? I don't see it.
The last part is potentional energy of bead, I understand.

I wrote it there:

So, could you tell me, if this Lagrangian right? And if it is not, how it has to look?
Thank you.

 

[Orodruin]

I suggest you write the position of the bead (both horizontally and vertically) as a function of the generalised coordinates. Differentiating it wrt time will give you the velocity.