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If we replace L with h in equation (44), we
can write the period as 8 Figure 8 A diagram of a physical pendulum with the
corresponding forces acting on the pendulum.
http://upload.wikimedia.org/wikipedia/commons/thumb/3/
39/Physical-Pendulum-Labeled-Diagram.png (48) 2 As with the simple pendulum, I is the rotational inertia of the pendulum about the pivot point. However, I
is NOT simply mh2 (it depends on the shape of the physical pendulum), but it is still proportional to m.
A physical pendulum will not swing if it pivots at its center of mass. Formally, this corresponds
to putting h=0 into equation (48). That equation then predicts that the period goes to infinity, which
implies that such a pendulum will never complete one swing.
Corresponding to any physical pendulum that oscillates about a given pivot point with period T is
a simple pendulum of length Lo with the same period T. We can find Lo from equation (47). The point
along the physical pendulum at distance Lo from the pivot point is called the center of oscillation of the
physical pendulum.
2.5.3 Measuring the Acceleration of Gravity using a Physical Pendulum We can use a physical pendulum to measure the free-fall acceleration g at a particular location on
Earth’s surface. 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 equation (48), the distance between the pivot point and the
center of mass is 1
2 (49) Recall that in, Table 1 from the angular motion lab the rotational inertia of a long thin rod about a
perpendicular axis through its center of mass is 1
12 (50) From the parallel-axis theorem, (51)
we find that the rotational inertia about a perpendicular axis through one end of the rod is 1
12 1
2 1
3 (52)
(53) Placing equations (49) and (53) into equation (48) and solving for g we find that
(54) 3 Thus by measuring L, and the period T or frequency, 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.) 9 2.6 Pendul...

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