Sapling Learning A 95.1-kg horizontal circular platform rotates freely with no f

Question

Sapling Learning A 95.1-kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.51 rad/s. A the platform at 4/5 of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 20.3 kg, drops vertically to the edge of the platform, grasps it, and continues to rotate with the platform. Find the angular velocity of the platform with its load. Model the platform as a disk of radius 1.79 m. drops a 8.01-kg bunch of bananas vertically onto the platform. They hit Number 1.08 rad/s hint by clicking on the on the bottom qd to hide the hint exil

Explanation / Answer

Using angular momentum conservation

Li = Lf

Ii*wi = If*wf

Ii = Moment of inertia of platform = 0.5*Mp*R^2

If = Moment of inertia of (platform + monkey + banana) = 0.5*Mp*R^2 + Mm*R^2 + Mb*(4R/5)^2

wi = initial angular velocity = 1.51 rad/sec

So,

wf = Ii*wi/If

wf = 1.51*(0.5*95.1*R^2)/(0.5*95.1*R^2 + 20.3*R^2 + 8.01*16*R^2/25)

wf = 1.51*0.5*95.1/(0.5*95.1 + 20.3 + 8.01*16*0.04)

wf = 0.984 rad/sec

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