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115. Problem 16.67E (HRW) A pendulum consists of a uniform disk with radius 10.0 cm and mass 500 g attached to a uniform rod with length 500 mm and mass 270 g. We have to calculate (a) the rotational inertia of the pendulum about the pivot; (b) the distance between the pivot and the centre of mass of the pendulum; (c) the period of oscillation.
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Solution: Click For PDF Version (a) Distance of the centre of the disk from the pivot,
Rotational inertia of a rod of length
Therefore, the rotational inertia of the physical pendulum about the pivot
(b) Using the definition of the CM and measuring distances from the pivot, the distance of the CM of the pendulum from the pivot is
(c) Period of oscillation of the pendulum
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Mass of the disk
and its
radius
.
Therefore the rotational inertia of the disk about the pivot will be
and mass
about
one of its ends is
