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The actual marry-go-round disk is the total weight - two persons. Which is 560-50 = 510 kg. So, Wouldn't the moment of inertia have to be (2.5)^2(510/2 + 2(25)? I don't understand why you used 560 when calculating the moment of inertia.

Hi theovilous, thanks for the question. What I'm seeing is that the text says

Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 560 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge.

which gives 560kg as the mass of the merry-go-round disk, not including the children. Perhaps you read that differently and interpreted that the children were included in the 560kg?

Best wishes,
Mr. Dychko

I read the question wrong! thanks for pointing that out! Thank you so much as always!!

My pleasure!