A94.7 kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.75 rad/s1.75 rad/s . a monkey drops a 9.25 kg9.25 kg bunch of bananas vertically onto the platform. they hit the platform at 4545 of its radius from the center, adhere to it there, and continue to rotate with it. then the monkey, with a mass of 21.1 kg21.1 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 1.63 m.= rad/s

The angular velocity of the platform is 1.114 rad/s.

Explanation:

Step 1:  Given data

Mass of the horizontal circular platform = 94.7 kg

Mass of the monkey = 21.1 kg

Initial angular velocity = 1.75 rad/s

A monkey drops a 9.25 kg bunch of bananas

They hit the platform at 4/5 of its radius from the center

Model the platform as a disk of radius 1.63 m

Step 2: Calculate the moment of inertia of the disk

I = ½ * m * r² = ½ * 94.7 * 1.63² = 125.80

Step 3: Calculate the initial angular momentum

I = 125.80 * 1.75 = 220.15

Step 4: Calculate the moment of inertia for the bananas

For the bananas, r = 4/5 * 1.63 = 1.304 m

I = 9.25 * 1.304² = 15.73

Step 5: Calculate Moment of inertia for the monkey

I = 21.1 * 1.63² = 56.06

Step 6: Total moment of inertia = 125.80 + 15.73 + 56.06 = 197.59

Step 7: Calculate final angular momentum = 197.59 * ω

197.59 * ω = 220.15

ω = 220.15 / 197.59

This is approximately 1.114 rad/s.