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Answer:
The rotational inertia of the pendulum around its pivot point is .
Explanation:
The angular frequency of a physical pendulum is measured by the following expression:
Where:
- Angular frequency, measured in radians per second.
- Mass of the physical pendulum, measured in kilograms.
- Gravitational constant, measured in meters per square second.
- Straight line distance between the center of mass and the pivot point of the pendulum, measured in meters.
- Moment of inertia with respect to pivot point, measured in
.
In addition, frequency and angular frequency are both related by the following formula:
Where:
- Frequency, measured in hertz.
If , then angular frequency of the physical pendulum is:
From the formula for the physical pendulum's angular frequency, the moment of inertia is therefore cleared:
Given that ,
,
and
, the moment of inertia associated with the physical pendulum is:
The rotational inertia of the pendulum around its pivot point is .