A physical pendulum has two possible pivot points; one has a fixed position and the other is adjustable along the length of the pendulum, as shown in Fig. 17-39. The period of the pendulum when suspended from the fixed pivot is T. The pendulum is then reversed and suspended from the adjustable pivot. The position of this pivot is moved until, by trial and error, the pendulum has the same period as before–namely, T. Show that the free-fall acceleration g is given by in which L is the distance between the two pivot points. Note that g can be measured in this way without needing to know the rotational inertia of the pendulum or any of its other dimensions except L.

A physical pendulum has two possible pivot points; one has a fixed position and the other is adjustable along the length of the pendulum, as shown in Fig. 17-39. The period of the pendulum when suspended from the fixed pivot is T. The pendulum is then reversed and suspended from the adjustable pivot. The position of this pivot is moved until, by trial and error, the pendulum has the same period as before–namely, T. Show that the free-fall acceleration g is given by

in which L is the distance between the two pivot points. Note that g can be measured in this    way without needing to know the rotational inertia of the pendulum or any of its other dimensions except L.