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.

  • $\begingroup$ But there is a torque - what does the normal force do as the disk rocks back and forth? $\endgroup$ Nov 21, 2017 at 19:53
  • $\begingroup$ Oh, ok. I didn't realize that. Can it be written as $Rd\theta mg\cos\phi $? ($\phi$ is the inclination of the disk) $\endgroup$ Nov 21, 2017 at 20:01
  • $\begingroup$ It might be easier to just do this from the Lagrangian. The rotational KE in both the $\theta$ and $\phi$ directions is simple to write down, and the gravitational potential depends only on the height of the center of mass, which can be easily converted to a function of $\phi$. $\endgroup$ Nov 21, 2017 at 20:10
  • $\begingroup$ You might want to put a bounty on this question. It is interesting and complicated at once. $\endgroup$
    – Gert
    Nov 22, 2017 at 1:09
  • $\begingroup$ @probably_someone Would it be possible to solve this with normal high school level physics, like F = ma net torque = Ialpha, I don't know about stuff like euler angles or lagrangian (yet) Can you write an answer for it? $\endgroup$
    – Rick
    Dec 17, 2017 at 7:58


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