A physical pendulum in the form of a planar object moves in simple harmonic motion with a frequency f. The pendulum has a mass m, and the pivot is located a distance d from the center of mass. Determine the moment of inertia of the pendulum about the pivot point

Explanation:

The moment of inertia (I) of the pendulum can be found using the following equation:

Where:

T: is the period of the pendulum

m: is the pendulum's mass

g: is the gravity

d: is the distance of the pivot from the center of mass

Solving the above equation for I:

    (1)

We have that the pendulum moves in simple harmonic motion with a frequency f, and this f is equal to:

By entering T into equation (1) we have:

Therefore, the moment of inertia of the pendulum about the pivot point is .

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