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How could you use a torsional pendulum to determine the rotational inertia of any object that could be mounted on the Rotary Motion Sensor?`
Note: The Vernier Rotary Motion Sensor is a bidirectional angle sensor designed to measure rotational or linear position, velocity and acceleration.
from the theory you obtain this linear differential equation
$$I\,\ddot\theta+k\,\theta=0$$
hence $$\omega^2=\left(\frac{2\pi}{T}\right)^2=\frac{k}{I}\quad\Rightarrow I=k\,\left(\frac{T}{2\,\pi}\right)^2$$
this means that to obtain the inertia $~I~$ you have to measure the period $~T~$ of the oscillation .
notice
to obtain linear oscillation the length of the rod must be much bigger then the radius of the rod and of course you have to know the stiffness $~k~$ of the rod. addition the proband must be mounted symmetric to the torsion axes.
