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User:CosineKitty/MathPage

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I am using this page to learn about mathematical markup.

Point mass ideal pendulum, small angle case:

Distributed mass pendulum, with moment of inertia, small angle case:

Equating the right hand sides of both of these equations, canceling like terms, and squaring both sides:

The ratio of moment-corrected gravity over experimentally determined gravity is:

For a cylinder rotating about an axis passing through its diameter at its center of gravity:

Using the parallel axis theorem, I move the rotation axis from center of gravity to the pivot point a distance L above the center of gravity:

Substituting the rightmost expression for I into the gi/gc equation, we get:

Buoyancy of air requires a correction of:

General formula for zero-angle limit of a conical pendulum consisting of a thin rod with an arbitrary linear density: