Question

How might you determine experimentally the moment of inertia of an irregularly shaped body about a given axis?

Short answer

The parallel-axis theorem can be used to determine the moment of inertia of an irregularly shaped body about a given axis.

Step-by-step solution

Concept/Significance of Moment of inertia

The moment of inertia is equal to the product of the sum of the masses of the different particles and the square of the distance from the axis of rotation.

Explain the method that can be used to determine the moment of inertia of an irregularly shaped body about a given axis

It is experimentally very easy to determine the moment of inertia about an axis passing at the edge of the body. Apparatuses doing typically accelerate the body, and then by finding the energy given to the system and the angular speed gained, the moment of inertia can be calculated.

In this case, however, the body is irregular and the axis is arbitrary. First, measure the moment of inertia about an axis passing at an edge of the body, but being parallel to the axis is required. Then, knowing the distance between the axis, the moment of inertia can be calculated from the parallel-axis theorem.

$I=I_0+m{d}^2$

Therefore, by using parallel-axis theorem, the moment of inertia of an irregularly shaped body about a given axis can be determined.