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# Problem: A uniform steel bar swings from a pivot at one end with a period of 2.1s? How long is the bar?

###### FREE Expert Solution

This is a pendulum problem.

Periodic time:

$\overline{){\mathbf{T}}{\mathbf{=}}{\mathbf{2}}{\mathbf{\pi }}\sqrt{\frac{\mathbf{I}}{\mathbf{m}\mathbf{g}\mathbf{R}}}}$ where I is the moment of inertia of the bar, m is its mass, g is gravitational acceleration, and R is the distance between the pivot and the center of mass.

Moment of inertial of a rod about the end:

$\overline{){\mathbf{I}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{3}}{\mathbit{m}}{{\mathbf{L}}}^{{\mathbf{2}}}}$ where m is the mass and L is the length.

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###### Problem Details

A uniform steel bar swings from a pivot at one end with a period of 2.1s? How long is the bar?