Question

# A 97.3-kg horizontal circular platform rotates freely with no friction about its center at an initial...

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.

given

Ro= 1.73 m ,

mo = 97.3-kg ,

o = 1.53 rad/s

and

m1 = 8.69 kg ,

R = 4/5 Ro ,

m2 = 21.9 kg

we have equation

Lo = I o = 1 /2 mo Ro2o

here considering the angular momentum is conserved

L0 = L1

where L1 = 1/2 mo Ro21 + m1 R121

even Lo = L2

where L2 = ( 1/2 mo Ro2 )2 + ( m1 R12) 2 + ( m2 Ro2 ) 2

Lo = L2

1 /2 mo Ro2o = ( 1/2 mo Ro2 )2 + ( m1 R12) 2 + ( m2 Ro2 ) 2

2 = moo / ( mo + (32/25) m1 +2 m2 )

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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