Question

If two children, with masses of 16 kg and 25 kg, sit in seats opposite one another in a rotating merry-go-round with an arm length of 1.5 m from the origin, what is the moment of inertia about the rotation axis?

Answer 1

`92.25 kgm^2`

Step-by-step explanation:

Assume both children bodies are point particles. The total moment of inertia about the rotation axis of 2 points particles of mass 16 kg and 25 kg at 1.5 m arm length is

`\sum I = m_1r_1^2 + m_2r_2^2`

where
`m_1 = 16 kg, m_2 = 25 kg` are the masses of 2 children
`r_1 = R-2 = 1.5m` are their distance to the center of rotation

`\sum I = 16*1.5^2 + 25*1.5^2 = 1.5^2(16 + 25) = 92.25 kgm^2`