A playground toy has four seats, each 5.6kg , attached to very light rods of len

Question

A playground toy has four seats, each 5.6kg , 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 24kg , sit in seats opposite one another, what is the moment of inertia about the rotation axis?

A playground toy has four seats, each 5.6kg , 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 24kg , sit in seats opposite one another, what is the moment of inertia about the rotation axis?

Explanation / Answer

Total Moment of Inertia, I = s1 + s2 + s3 + s4

(The total moment of inertia is equal to the sum of the four seat's moments of inertia.)

For the first two seats, which we shall say are empty, they each equal (M = mass, R = radius),

         s1, s2 = M * (R^2) = 5.6 * (1.5^2) = 12.6

Each of the next seats have children in them, so we have to add the masses of the children to the masses of the seats.

s3 = M * (R^2) = (5.6 + 16) * (1.5^2) = 48.6

s4 = M * (R^2) = (5.6 + 24) * (1.5^2) = 66.6

And then add them all up.

I = s1 + s2 + s3 + s4 = (12.6) + (12.6) + (48.6) + (66.6) = 140.4 kg m^2

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