RollingVsInertia.gif (506 × 311 pixels, file size: 695 KB, MIME type: image/gif, looped, 74 frames)
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Summary
DescriptionRollingVsInertia.gif |
English: Cylinders with the——same mass. But different moments of inertia will roll down a flat surface at different accelerations, as they have——to "convert" different amounts of potential energy into kinetic energy——to achieve a given angular velocity. |
Date | |
Source | https://twitter.com/j_bertolotti/status/1225050271384002561 |
Author | Jacopo Bertolotti |
Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code
s1※ := R1 \※1※; x1※ := x10 + s1※ Cos※] + R1 Sin※]; y10 = Abs※ Tan※]; y1※ := y10 - s1※ Sin※] + R1 Cos※]; T1※ := 1/2 m1 (D※, t]^2 + D※, t]^2) + 1/2 I1 (D※1※, t])^2; V1※ := m1 g y1※; L = FullSimplify※ - V1※] eq1 = FullSimplify※1'※], t] - D※1※]] m1 = 1; R1 = 1; g = 1; \※ = \※/6; x10 = -20; sol = Table[ NDSolve※1※ == 0, \※1'※ == 1}, {\※1※}, {t, 0, 20}], {j, 0, 5}]; dim = Dimensions※※]; \※ = 2; p1 = Table[ Legended[Graphics3D[{ Gray, Polygon※, 0}, {1.2*x10, \※, 1.2 y10}, {1.2*x10, (dim + 1) \※, 1.2 y10}, {0, (dim + 1) \※, 0}}], Table※, Cylinder※, \※ j, y1※}, {x1※, \※ (j + 1), y1※}} /. sol※]) /. {t -> \※}, R1]}, {j, 1, dim}]}, Boxed -> False], PointLegend※, {j, 1, dim}] , Table※\) I=", ToString※, "\!\(\*SubscriptBox※\)"], {j, 1, dim}], LegendMarkerSize -> 20, LabelStyle -> {FontFamily -> "Times"}] ] , {\※, 0, 7.3, 0.1}]; ListAnimate※
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current | 09:24, 6 February 2020 | ![]() | 506 × 311 (695 KB) | Berto | User created page with UploadWizard |
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