stion f 20 15 Sapling Learning A 87.5-kg horizontal circular platform rotates fr

Question

stion f 20 15 Sapling Learning A 87.5-kg horizontal circular platform rotates freely with no friction about its center at an initial anqular 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 21.9 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 drops a 9.87-kg bunch of bananas vertically onto the platform. They hit of radius 1.65 m. Number rad/s

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*87.5*R^2)/(0.5*87.5*R^2 + 21.9*R^2 + 9.87*16*R^2/25)

wf = 1.51*0.5*87.5/(0.5*87.5 + 21.9 + 9.87*16*0.04)

wf = 0.917 rad/sec

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