a 94.5 kg horizontal circular platform rotates freely with no friction about its

Question

a 94.5 kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.69 rad/s . A monkey drops a 8.59 bunch of bananas vertically onto the platform A 94.5-kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.69 rad/s. A the platform at 4/5 of its radius from the center, adhere to it there, and continue to rotate wi monkey, with a mass of rotate with the platform. Find the angular velocity of the platform with of radius 1.87 m. ey drops a 8.59-kg bunch of bananas vertically onto the platform. They hit 1.7 kg, drops vertically to the oo radiwis 1 tre matform. Find the angular velocity of the platform with its loadMeheplaom as a disk its load. Model the platform as a Number rad/s

Explanation / Answer

The initial angular momentum is

L = I = ½ m R ²

m = 94.5 kg

R = 1.87 m

= 1.69 rad / s

angular momentum is conserved
L = L

L = ( ½ m R ² ) + ( m R ² )

m = 8.59 kg

R = ( 4/5) R

L = L

L = ( ½ m R ² ) + ( m R ² ) + ( m R ² )

½ m R ² = ( ½ m R ² ) + [ m ( / ) ² R ² ] + ( m R ² )

m R ² = [ m + 2 m ( 16/25 ) + 2 m ] R ²

m = [ m + 2 m ( 16/25) + 2 m ]

= m / [ m + (32/25 ) m + 2 m ]

m + ( 32/25 ) m + 2 m

= 103.09kg + ( 32/25 ) (8.59 kg ) + 2 ( 21.7kg )

= 157.4852 kg

= (103.09kg ) ( 1.87 rad / s ) / 157.4852kg

= 1.22 rad /s

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