We can use a physical pendulum to measure the free-fall acceleration g at a panicular location on Earth’s surface. (Countless thousands of such easurements have been made during geophysical prospecting.) To analyze a simple case, take the pendulum to be a uniform rod of length L suspended from one end. For such a pendulum, h in the distarice between the pivot point and the center of mass, is. Table tells us thilt the rotational inertia of this pendulum about a perpendicular- axis through its center of mass is From the parallel-axis theorem of (I = leom + Mh2), we then find that the rotational inertia about a perpendicular-axis through one end of the rod is I = leom + mh2 = nmLl + m(!L)2 = tmLl. If we put h = 1L and I = ~mL2 in and solve for we find
Thus, by measuring L and the period T, we can find the value of g at the pendulum’s location. (If precise measurements are to be made, a number of refinements are needed, such as swinging the pendulum in an evacuated chamber.