# Motion of wobbling plates [closed]

This is a common phenomenon that I observe whilst preparing a meal. Assume that we have a plate of diameter $r$ and we drop it when there is an angle $\theta$ between it and the table and we also apply a force $F$ at the side of the plate.

Suppose that the gravitational acceleration is $g$ how can we determine this plates "wobbling" frequency, how this frequency depends on time and when would this motion stop?

https://drive.google.com/open?id=0B2pRI_pd_h4-WW5ZaHJHay0zQW8 video of the action called as "wobbling"

• Welcome to Physics SE! Please note that we don't answer homework or worked example type questions. Please see this Meta post on asking homework/exercise questions and this Meta post for "check my work" problems. Mar 1, 2017 at 15:00
• This is not actually a homework question. I have gave letters just for the ease of discussion.
– user147133
Mar 1, 2017 at 15:01
• Richard Feynman wrestled with a similar problem, although his plate was wobbling in the air while spinning. If you can get this article from the American Journal of Physics 75, 665 (2007), it undoubtedly will help you understand the complexity of this problem: aapt.scitation.org/doi/abs/10.1119/1.2402156?journalCode=ajp Mar 1, 2017 at 15:16
• Unfortunately I cannot. Which link I click on the site you suggested it comes back to the actual website you gave.
– user147133
Mar 1, 2017 at 15:51
• Possible duplicate of What is the physics of a spinning coin? Mar 2, 2017 at 10:17

The problem is known as "Euler's disk", and a detailed analysis of the motion is given on this page - the conclusion is that the rate of rotation as a function of angle $\theta$ is given by
$$\omega = \sqrt{\frac{4g}{r\sin\theta}}$$