Curvilinear One Dimensional System

[kala]

Homework Statement

There is a child's toy, which has the shape of a cylinder mounted on top of a hemisphere (the picture the book has looks like a half of a circle with a square on top.). The radius of the hemisphere is R and the CM of the whole toy is at a height h about the floor. (this in the picture has the half circle's radius is R and then above that is the CM which is at height h.) Write down the gravitational potential energy when the toy is tipped to an angle theta from the vertical. The book gives a hint and says that you need to find the height of the CM as a function of theta.

Homework Equations

P=mgh is potential energy

The Attempt at a Solution

I am just having trouble deciding if my h is correct. I think that
h=(R+b)cos theta+ r*theta*sin theta where b is the distance from R to the CM.
Is this right?

 

[turin]

I don't know what you mean by "the distance from R". I am thinking in terms of the CM of the cylinder only. I would say that I have something similar to what you have.