I'm new with rigid problems about. I'm trying to solve this:
A massive circular disk of mass m, radius R, and negligible thickness is leaned against a vertical wall, slanting by 45 . In the gravitational field, it can oscillate, rolling without slip on the ground and along the wall.
I need to write down the equations of motion of the disk.
I try to use the Euler's equations. Since there's no torque, $I_1=I_2 \neq I_3 $, and $ \omega_1=\omega_2=0$ ($\omega_2$ is the desired angular speed) Therefore $$I_2\dot\omega_2=0 \Rightarrow \omega=kte$$
But this is not useful because obviously the motion is an oscillatory one.
How to write the equation of motion of this?
Any suggestions would be very welcome.
I don't want that you solve this for me. I want to understand how to get the equations.