Answer:
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.
