Question

A 80.5 kg horizontal circular platform rotated freely with no friction about its center at an initial angular velocity of 1.77 rad/s. A monkey drops a 9.75 kg bunch of bananas vertically onto the platform. They hit the platform at 4/5 of its radius from the center.

a. The angular velocity of the platform increases.
b. The angular velocity of the platform decreases.
c. The angular velocity of the platform remains unchanged.
d. The angular velocity of the platform depends on the speed of the falling bananas.

Answer 1

The angular velocity of the platform decreases when the monkey drops the bunch of bananas onto it.

Step-by-step explanation:

The angular velocity of the platform decreases. When the monkey drops the bunch of bananas onto the platform, the platform experiences an increase in torque, causing it to slow down. This is due to the conservation of angular momentum. The initial angular momentum of the platform without the bananas is given by:

Angular momentum (1) = moment of inertia (I) x initial angular velocity (ω)

After the bananas are dropped, the total moment of inertia of the system increases since the bananas add to the rotational mass. However, the angular momentum needs to remain constant, so the angular velocity of the platform decreases.