Aplayground toy has four seats, each 6.4kg , attached to very light rods of length r= 1.5m , as seen from below in the figure.
if two children, with masses of 16kg and 23kg , sit in seats opposite one another, what is the moment of inertia about the rotation axis?

The moment of inertia about the rotation axis is 145.35 kg.m²

Explanation:

Given:

Mass of each seat = 6.4 kg

length of rods attached to the seat = radius of the seat from center = 1.5m

Moment of inertia = M₁r²

Moment of inertia about the first child:

total mass at that point = mass of the child + mass of the seat

                                      = 16kg + 6.4 kg = 22.4 kg

Moment of inertia at the point where the first child sits = 22.4 *1.5²

= 50.4 kg.m²

Moment of inertia about the second child:

total mass at that point = mass of the child + mass of the seat

                                       = 23kg + 6.4 kg = 29.4 kg

Moment of inertia at the point where the second child sits = 29.4 *1.5²

= 66.15 kg.m²

Moment of inertia about the two empty seats:

Moment of inertia about the two seats = 2(6.4*1.5²)

= 28.8 kg.m²

Moment of inertia about the rotation axis = Moment of inertia about the point of two children + moment of inertia about the two seat

= (50.4 + 66.15 + 28.8) kg.m²

= 145.35 kg.m²

Therefore, the moment of inertia about the rotation axis is 145.35 kg.m²

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explanation: