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**Hi everybody, I know this problem has been posted before, but it envolved Lagrangian methods which I haven't seen yet. I would appreciate any help.**

1. Homework Statement

1. Homework Statement

A small hoop is rolling without slipping on a bigger cylinder which is stationary. I need to write Newton's Laws and Torques, and find out at what angle the small cylinder falls off the bigger one.

## Homework Equations

##ζ=Iα##

##F=ma##

##I_{cm}= ma^2##

## The Attempt at a Solution

My restrain equation, since it rolls without slipping is that ##Φ=\frac{(R+a)}{a}θ## , because I'm taking θ=0 at the top.

##\hat{θ}) Fr- mg sinθ=m(R+a) \ddot{θ}##

##\hat{r}) N-mgcosθ=-m(R+a) \dot{θ}^2##

And around the center of mass of the small cylinder, the only force that makes a torque is friction, so

##ζ=I\ddot{Φ}##

##-aFr \hat{k} = -ma^2 \ddot{Φ} \hat{k} = -m a^2 \frac{(R+a)}{a} \ddotθ## So,

##Fr=m \frac{a^2}{a} \frac{(R+a)}{a} \ddotθ = m(R+a) \ddotθ##

And replacing this in my theeta equation I get:

##\hat{θ}) m(R+a) \ddot{θ} - mg sinθ=m(R+a) \ddot{θ}##

And this is where I get confused, becuse I get ## mgsinθ=0## I now I'm making a silly mistake somewhere, like the direction of a vector or something, but I cannot see it. Thanks in advance.