**Unformatted text preview: **t the moment of inertia of a thin rod about its end is 1
3 (75) and the moment of inertia of a mass about an axis is (76)
13 Thus the total inertia I is given as 1
3 (77) Therefore we can write the frequency of the physical pendulum as 1
2 (78) 1
3 Now we must find h which is the system of mass for the entire physical pendulum. The first thing
that we do is that we draw the system (See Figure 12) and find the positions of the center of mass for each
object in the system. In our case, we have two objects, the rod and the mass. Therefore the center of mass
of the rod of length L is 2 (79) Next, we find the center of mass of the mass. This is simply the length from the center of mass to the end
of the rod. We define this length to be D, thus the mass center of mass is given by (80)
Therefore we can write the center of mass, h, of the entire system as (81)
2 (82) Now that you know how to find the distance to the center of mass of the system, you can
calculate the theoretical frequency. You should notice that, you can also measure the acceleration of
gravity by solving for g in equation (78). This would yield 2 1
3 (83) 14 Figure 12 Diagram of center of
mass of the physical pendulum.
Here L is the length of the rod
thus the center of mass of the rod
is exactly in the middle. D is the
distance to the middle of the brass
weight so the center of mass is
exactly in the middle of the
weight. Finally h is the center of
mass of the system of the rod and
weight together. 15...

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