Question

A 97.3-kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.53 rad/s. A monkey drops a 8.69-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 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 of radius 1.73 m.

Answer #1

given

R_{o}= 1.73 m ,

m_{o} = 97.3-kg ,

_{o} =
1.53 rad/s

and

m_{1} = 8.69 kg ,

R = 4/5 R_{o} ,

m_{2} = 21.9 kg

we have equation

L_{o} = I _{o} = 1
/2 m_{o} R_{o}^{2}_{o}

here considering the angular momentum is conserved

L_{0} = L_{1}

where L_{1} = 1/2 m_{o}
R_{o}^{2}_{1} +
m_{1} R_{1}^{2}_{1}

even L_{o} = L_{2}

where L_{2} = ( 1/2 m_{o}
R_{o}^{2} )_{2} + (
m_{1} R_{1}^{2}) _{2} + (
m_{2} R_{o}^{2} ) _{2}

L_{o} = L_{2}

1 /2 m_{o} R_{o}^{2}_{o}
= ( 1/2 m_{o} R_{o}^{2} )_{2}
+ ( m_{1} R_{1}^{2}) _{2} + (
m_{2} R_{o}^{2} ) _{2}

_{2} =
m_{o}_{o} / (
m_{o} + (32/25) m_{1} +2 m_{2} )

_{2} =
97.3 X 1.53 / ( 97.3 + (32/25) 8.69 + 2 X 21.9 )

_{2} =
148.869 / 152.2232

_{2} =
0.977 rad/sec

**the angular velocity of the platform with its load
is _{2} =
0.977 rad/sec**

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