10.10 : Moment of Inertia of Compound Objects

The moment of inertia is a quantitative measure of the rotational inertia of an object. It is defined as the sum of the products obtained by multiplying the mass of each particle of matter in a given body by the square of its distance from the axis. The total moment of inertia for compound objects can be found by determining and adding the moment of inertia of individual components together.

Consider a child of mass (m_c) 25 kg standing at a distance (r_c) of 1 m from the axis of a rotating merry-go-round. The merry-go-round is approximated as a uniform solid disk with a mass (m_m) of 500 kg and a radius (r_m) of 2 m. Find the moment of inertia of the compound system.

The total moment of inertia of the system can be determined by adding up the individual moments of inertia of the merry-go-round and the child rotating on the axis. Since the mass and size of the child are much smaller than the merry-go-round, the child can be considered as a point mass.

1. The moment of inertia (I) for the child is calculated as

2. The moment of inertia (I) for the merry-go-round is calculated as

3. By substituting and adding both values, the total moment of inertia of the system is determined to be 1025 kg⋅m².

This text is adapted from Openstax, University Physics Volume 1, Section 10.5: Calculating Moments of Inertia.