A Texas cockroach first rides at the center of a circular disk thatrotates freel

Question

A Texas cockroach first rides at the center of a circular disk thatrotates freely like a merry-go-round without external torques. Thecockroach then walks out to the edge of the disk, atradius R. The scale on the axis is setby a=1.2 rad/s and b=1.6rad/s. When the cockroach is on the edge atradius R, what is the ratio of the bug's rotationalinertia to that of the disk, both calculated about the rotationaxis?

I submitted answers 1.3 and it was graded as wrong and 0.3 is alsograded as wrong. Please let me know how to do this question and thefinal answer.

Explanation / Answer

Given : a=1.2 rad/s and b=1.6rad/s    From the conservation of angular momentum I1 a = I2b I2 / I1 = a /b            = 1.2 rad/s / 1.6 rad/s            = 0.75 I hope it helps you

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