Rigid body rotation is defined by a circular velocity field and an acceleration field comprising Euler acceleration (changes in spin) and centripetal acceleration (inward pull). This velocity field is incompressible, while the acceleration field exhibits negative divergence, reflecting the constant inward force required to maintain the rotation. In a rotating frame, pseudo-forces are conservative, meaning work depends only on an object's distance from the center. Notably, the Coriolis force does zero work, allowing energy to be perfectly conserved between radial motion and centrifugal potential energy. This potential energy creates a "potential well" for orbiting bodies, where the inward pull of gravity is balanced by an outward centrifugal barrier. Because this barrier grows faster than gravity at close range, it acts as a shield that prevents orbital collapse, keeping planets "sloshing" within a stable valley.
block-beta
columns 6
CC["Criss-Cross"]:6
%% Condensed Notes
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RF["Relevant File"]:6
NV["Narrated Video"]:6
PA("Plotting & Analysis")AA("Animation & Analysis")KT("Summary & Interpretation") ID("Illustration & Demo") VA1("Visual Aid")MG1("Multigraph")
%% Proof and Derivation
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AF("Derivation Sheet"):6
NV2["Narrated Video"]:6
PA2("Plotting & Analysis")AA2("Animation & Analysis")KT2("Summary & Interpretation") ID2("Illustration & Demo")VA2("Visual Aid") MG2("Multigraph")
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%% %% Condensed Notes
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%% Proof and Derivation
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