Consider a merry-go-round that has the form of a disc with radius 5.6 m and mass 140 kg. If two children, each of mass 20 kg, sit on the outer edge of the merry-go-round, what is the total moment of inertia

3449.6 kgm²

Explanation:

Given that

Radius of the merry go round, r = 5.6 m

Mass of the merry go round, M = 140 kg

Mass of the children, m = 40 kg

Total moment of inertia, I = ?

The total moment of inertia is given as the sum of moments of inertia of the merry-go-round in addition to that of the child. Mathematically, we say

I = 1/2Mr² + mr²

I = 1/2 * 140 * 5.6² + 40 * 5.6²

I = 70 * 31.36 + 40 * 31.36

I = 2195.2 + 1254.4

I = 3449.6 kgm²

Therefore, the total moment of inertia of the merry go round and that of the children on it is 3449.6 kgm²