A 98.1 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 9.29 kg bunch of bananas vertically onto the platform. They hit the platform at 45 of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 20.3 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 1.51 m.

Question

Physics

Maxwell Marquez

10 February, 16:16

A 98.1 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 9.29 kg bunch of bananas vertically onto the platform. They hit the platform at 45 of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 20.3 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 1.51 m.

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Dozer · Answer 1

The problem is based on conservation of angular momentum.

Moment of inertia of the disc = 1/2 m R², m is mass of the disc and R is its radius.

= 1/2 x 98.1 x 1.51²

= 111.84 kg m²

Moment of inertia of disc + moment of inertia of bananas + monkey

= 1/2 x 98.1 x 1.51² + 9.29 x. 45 x 1.51 + 20.3 x 1.51² (moment of inertia of banana and monkey will be equal to mass x radial distance from axis²)

= 111.84 + 6.31 + 46.28

= 164.43 kg m²

Now applying law of conservation of angular momentum

= I₁ ω₁ = I₂ω₂

111.84 x 1.69 = 164.43 x ω₂

ω₂ = 1.15 rad / s