# Analytic expressions of the kinetic and potential energy [closed] A homogeneous rigid circular disc (radius R, mass ms, center point S) rolls without a slip on a plain with a small angle of inclination alpha against the horizontal. A point mass MG is fixed on the disc in a distance e to the center point S. The motion of the disc can be described by the angle phi between the vertical and the connection line SMG.

Please see the figure for reference.

I am trying to calculate Kinetic Energy and Potential energy of the given problem (pic #2) and I have considered both masses as one system but I am not sure if that's correct or not. Also, I am not sure if the h term in potential energy (mgh) is correct here. So I would be glad if someone could throw some light on this. Thanks in advance!

## closed as off-topic by Carl Witthoft, BarbalatsDilemma, Fred, OpticalResonator, MarkAug 13 '18 at 14:34

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question does not appear to be about engineering, within the scope defined in the help center." – Carl Witthoft, BarbalatsDilemma, Fred, OpticalResonator, Mark
If this question can be reworded to fit the rules in the help center, please edit the question.

• This is an obvious homework problem, and further is a Physics question, not Engineering. – Carl Witthoft Aug 10 '18 at 17:25

## 1 Answer

The calculations (in Mathematica) with minimal explanations. Hopefully you can pick it up from here. • Thanks for your answer. I totally understand Ps and I don't get how you calculated Pg. Can you please elaborate ? – MechNovice Aug 11 '18 at 9:14
• $p_g$ is the sum of vectors $p_s$ and the position $\{e \sin (\alpha ),-e \cos (\alpha )\}$ of $MG$ w.r.t the center of $Ms$. The latter is in a different coordinate system that rotates with the $Ms$. Hence the rotation matrix to get both in the same coordinate system. – Suba Thomas Aug 13 '18 at 13:49