Measuring Moment of Inertia
The moment of inertia of a part around an axis can be determined experimentally by forming a compound pendulum. Suspend the part from a convenient pivot point P so that it swings freely in a plane perpendicular to the direction of the desired moment of inertia. Determine the distance r from the pivot point P to the center of mass C of the part. The equations of motion of a compound pendulum show that the natural frequency of oscillation of the part as it swings from the pivot point is given by
Thus, if the period of oscillation is measured to be τ = 2π/ω, then the moment of inertia about the pivot point is given by
The moment of inertia of the part about the center of mass, IC, is then determined using the parallel axis theorem,
The moment of inertia of complex systems such as a vehicle or airplane around its vertical axis can be achieve by suspending the system from three points to form a trifilar pendulum. The period of oscillation of the trifilar pendulum yields the moment of inertia of the system.
Experimental procedures to measure the moment of inertia about three perpendicular axes for complex systems are described in the article NACA Technical Note No. 1629.
Read more about this topic: Inertia Tensor, Scalar Moment of Inertia of A Rigid Body
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