Passage VII

A physical pendulum is an object that is suspended vertically from a rigid support (see example in Figure 1).

L is the distance between the rod (the rigid support) and the pendulum's center of mass (CM). When the pendulum is displaced from its equilibrium position and then released, it oscillates (swings back and forth) about the rod, which acts as the axis of rotation.

Students tested several types of physical pendulums. In each trial, first, they computed the moment of inertia, I, in kilogram meters² (kg m²), of a pendulum. (I is a measure of the mass of a pendulum and how the mass is distributed. ) Next, they displaced the pendulum slightly from its equilibrium position, released it, and measured the time, in seconds, it took the pendulum to oscillate through 20 cycles (1 cycle is 1 round-trip back and forth). Finally, they computed the pendulum's average period, P (the average time it took to complete 1 cycle) .

Study 1

In Trials 1-5, each pendulum was a 1.0 kg solid sphere with a diameter, D, of 0.20 m(see Figure 2).

Each pendulum, however, had a different L. The results are shown in Table 1.

Study 2

In Trials 6-10, each pendulum was a 1.0 kg thin, flat circular plate with D = 0.20 m (see Figure 3).

Each pendulum had a different L (see Table 2) .

Study 3

In Trials 11-15, each pendulum was a 1. 0 kg thin, spherical shell with D = 0.20m (see Figure 4).

Each pendulum had a different L (see Table 3).