# Geometry of problem

1. Dec 12, 2011

### Xyius

This is a Lagrangian problem, I am posting it here in introductory physics because what I need help with isn't in Lagrangian mechanics, but rather geometry.

http://img97.imageshack.us/img97/7504/what3.png [Broken]

I am confused as how they got those relations for x and y. I have tried to make sense out of it but cannot figure it out. I am sure it is something really simple!

Last edited by a moderator: May 5, 2017
2. Dec 12, 2011

### gnulinger

Let's start with y. You can probably understand where the (r+b)cos(θ) comes from I hope. Now imagine that you roll the cube around the sphere by an angle θ. The length of the line CB is then what? That's right! It's rθ. So obviously this adds a height rθsin(θ). Now you have

$$y = (r+b)cos(θ) + rθsin(θ)$$

3. Dec 12, 2011

### Joffan

Hm. I agree with Xyius; I don't think that, as stated, the formula necessarily holds. Consider a much smaller cube in the same place, at the same angle.

The unstated assumption is that the cube was originally placed square and centered on top of the cylinder and rolled to its current location, but that hasn't been specified.

4. Dec 13, 2011

### gnulinger

A much smaller cube would not be able to get to as large of an angle, because the cube must roll without slipping. The formula is valid.

5. Dec 13, 2011

### Xyius

Ah! I understand now! Thank you very much :]