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I am fairly new to Mathematica.

I am trying to model an ideal cylinder of uniform density of radius R (any arbitrary value) which has a cylinder of radius R/2 missing from it. The resulting solid is rolling in a straight line. The centre of mass is calculated to be R/6 from the point equidistance to the circumference of the larger circle.

How do I go about doing this? And how would I be able to show a graph of angular rotation between the line perpendicular to the x-axis and the line of symmetry of this system?

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  • $\begingroup$ I don't suppose this is a homework question...is it? You'll usually get more 'bites' if you also post code you tried yourself...and then show us where your attempt failed...but this is a fairly standard mechanics question, with even an equation of motion with an analytical solution...finding the equation and looking at the docuemntation for DSolve will get you pretty far. $\endgroup$ – morbo Jun 12 '19 at 21:46
  • $\begingroup$ A well-labeled diagram of the system would be helpful. $\endgroup$ – m_goldberg Jun 13 '19 at 2:29
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Here's how you begin:

    RegionPlot3D[
     y^2 + z^2 < 4 && 
     -2 < x < 2 && 
     y^2 + (z - .5)^2 > .5,
     {x, -3, 3}, 
     {y, -3, 3}, 
     {z, -3, 3},
     PlotPoints -> 100,
     PlotStyle -> Opacity[0.5]]

enter image description here

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