Elementary Mechanics for Engineering Students

Cover Elementary Mechanics for Engineering Students
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The quantity M r is called the statical moment; and the length of the physical pen- dulum then is numerically equal to the moment of inertia about the axis of suspension divided by the statical moment.
PENDULAR MOTION 87 Kater's Pendulum. The most accurate method for determining the acceleration of gravity is by means of a pendulum. But the only quantity in equation (n) that is readily determined by experiment is the time.
It is, however, possible by employing a Kater's, or reversible pendulum,
... to determine the length, without knowing the moment of inertia or statical moment. The following discussion will make this clear.
In Fig. 30, let a b be a rigid rod sup- " porting the two unequal masses m l and wi m 2, and let M be the mass of the whole _ system whose centre of mass is at C. Let this system be supported by an axis 5, then j the length of the equivalent simple pendu- _ lum is L = JTr> ' ' (I2) FIG. 30. Where I 8 is the moment of inertia of the system about the axis 5, and r the distance from the axis S to the centre of mass.


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