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

m₁ = 8.69 kg ,

R = 4/5 R_o ,

m₂ = 21.9 kg

we have equation

L_o = I _o = 1 /2 m_o R_o²_o   

here considering the angular momentum is conserved

L₀ = L₁

where L₁ = 1/2 m_o R_o²₁ + m₁ R₁²₁

even L_o = L₂

where L₂ = ( 1/2 m_o R_o² )₂ + ( m₁ R₁²) ₂ + ( m₂ R_o² ) ₂

L_o = L₂

1 /2 m_o R_o²_o = ( 1/2 m_o R_o² )₂ + ( m₁ R₁²) ₂ + ( m₂ R_o² ) <sub>2

2</sub> = m_oo / ( m_o + (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