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# Calculations & Error Propagation

By Trevor J. Hoglund, December 05, 2017

The moment of inertia for a cylinder (a rod $R$ whose thickness is not negligible) is given by the equation1

where $m$ is the mass of the cylinder, $r$ is the radius of the cylinder, and $t$ is half the length of the cylinder. In this specific case $m=0.030\pm0.0001kg$, $r=0.002\pm0.001m$, and $t=0.300\pm0.001m$. This yields a resulting moment of inertia of

The error on equation $2b$ is then computed using the general equation for error propagation:

such that

The combination of equations $2b$ and $4f$ gives a reported value for $I_R$ as