Final answer:
The new spin rate of the ride when all the children jump off is 0 rev/s.
Step-by-step explanation:
To find the new spin rate of the ride when all the children jump off, we need to use the concept of conservation of angular momentum. The initial angular momentum of the ride is equal to the final angular momentum of the ride. The initial angular momentum can be calculated by multiplying the moment of inertia of the ride with its initial angular velocity. The final angular momentum can be calculated by multiplying the moment of inertia of the ride with the final angular velocity.
Let me walk through the solution step by step. First, let's calculate the initial angular momentum:
Initial angular momentum = Moment of inertia x Initial angular velocity
Given that the moment of inertia of the ride is 4 x (mass of each spoke + mass of each pod). In this case, it would be 4 x (200.0 kg + 100.0 kg) = 1200.0 kg.
Given that the initial angular velocity of the ride is 0.2 rev/s.
Initial angular momentum = 1200.0 kg x 0.2 rev/s = 240.0 kg·m²/s
Now, let's calculate the final angular momentum:
Final angular momentum = Moment of inertia x Final angular velocity
Since all the children have jumped off, the moment of inertia of the ride remains the same, but the final angular velocity becomes zero (since the ride is not spinning).
Final angular momentum = 1200.0 kg x 0 rev/s = 0 kg·m²/s
According to the conservation of angular momentum, the initial angular momentum is equal to the final angular momentum:
240.0 kg·m²/s = 0 kg·m²/s
Since the final angular momentum is zero, the final angular velocity of the ride is also zero. Therefore, the new spin rate of the ride is 0 rev/s.