A 86.1-kg horizontal circular platform rotates freely with no friction about its

Question

A 86.1-kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.55 rad/s. A monkey drops a 8.79-kg bunch of bananas vertically onto the platform. They hit 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 20.5 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 1.67 m.

Explanation / Answer

The initial angular momentum is L = I = ½ m R ²
where
m = 99.3 kg
R = 1.75 m
= 1.55 rad/s

Using Conservation of Angular momentum
L = L1
where L1 = ( ½ m R ² ) + ( m R ² )
where
m = 8.11 kg
R = (4/5) R

when the monkey drops himself vertically to the edge of the platform and remains there, the total angular
momentum is still conserved L = L

where,
L = ( ½ m R ² ) + ( m R ² ) + ( m R ² )
½ m R ² = ( ½ m R ² ) + [ m (4/5)^2 R ² ] + ( m R ² )
m R ² = [ m + 2 m ( ¹ / ) + 2 m ] R ²
m = [ m + 2 m ( ¹ / ) + 2 m ]
= m / [ m + ( ³² / ) m + 2 m ]
= (99.3 * 1.55)/(99.3 + (32/25) * 8.11 + 2 * 20.3 )
= 1.024 rad/s

Angular velocity of the platform with its load, = 1.024 rad/s

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