enter image description hereA 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!

  • $\begingroup$ This is an obvious homework problem, and further is a Physics question, not Engineering. $\endgroup$ Aug 10, 2018 at 17:25

1 Answer 1


The calculations (in Mathematica) with minimal explanations. Hopefully you can pick it up from here.

enter image description here

  • $\begingroup$ Thanks for your answer. I totally understand Ps and I don't get how you calculated Pg. Can you please elaborate ? $\endgroup$
    – MechNovice
    Aug 11, 2018 at 9:14
  • $\begingroup$ $p_g$ 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. $\endgroup$ Aug 13, 2018 at 13:49

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