In a physics lab experiment for the determination of moment of inertia, a team w

Question

In a physics lab experiment for the determination of moment of inertia, a team weighs an object and finds a mass of 2.42 kg. They then hang the object on a pivot located 0.202 m from the object's center of mass and set it swinging at a small amplitude. As two of the team members carefully count 123 cycles of oscillation, the third member measures a duration of 261 s. What is the moment of inertia of the object with respect to its center of mass about an axis parallel to the pivot axis? Number 0.076 kg .1n g In

Explanation / Answer

123 cycles in 261 seconds

so,

1 cycle in 261 / 123 sec

so time period = 261 / 123 sec

The period T of a compound pendulum is given by for sufficiently small oscillations Where, I is the moment of inertia of the pendulum about the pivot point, m is the mass of the pendulum, and R is the distance between the pivot point and the center of mass is given as

T = 2 * pi * sqrt(moment of inertia / (mass * g * radius))

261/123 = 2 * pi * sqrt(moment of inertia / (2.42 * 9.8 * 0.202))

moment of inertia = 0.546391 kg.m^2

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