A baggage carousel at an airport is rotating with an angular speed of 0.397 rad/s when the baggage begins to be loaded onto it. The moment of inertia of the carousel is 2440 kg·m2. Ten pieces of baggage with an average mass of 16.5 kg each are dropped vertically onto the carousel and come to rest at a perpendicular distance of 2.95 m from the axis of rotation. Assuming that no net external torque acts on the system of carousel and baggage, find the final angular speed.

Question

A baggage carousel at an airport is rotating with an angular speed of 0.397 rad/s when the baggage begins to be loaded onto it. The moment of inertia of the carousel is 2440 kg·m2. Ten pieces of baggage with an average mass of 16.5 kg each are dropped vertically onto the carousel and come to rest at a perpendicular distance of 2.95 m from the axis of rotation. Assuming that no net external torque acts on the system of carousel and baggage, find the final angular speed.

Answer 1

To find the final angular speed of the carousel, we can use the principle of conservation of angular momentum.

Angular momentum is calculated using the formula:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular speed.

The initial angular momentum of the carousel can be calculated as:

L_initial = I_initial * ω_initial

The moment of inertia of the carousel is given as 2440 kg·m^2, and the initial angular speed is 0.397 rad/s.

L_initial = 2440 kg·m^2 * 0.397 rad/s

Next, we need to calculate the angular momentum of the dropped baggage. The angular momentum of each piece of baggage can be calculated as:

L_baggage = m * r * v

where m is the mass of each baggage, r is the perpendicular distance from the axis of rotation, and v is the tangential velocity.

The tangential velocity can be calculated as:

v = ω * r

The average mass of each baggage is given as 16.5 kg, and the perpendicular distance from the axis of rotation is 2.95 m.

Using the calculated tangential velocity, we can find the angular momentum of each baggage.

L_baggage = 16.5 kg * 2.95 m * (ω_initial * 2.95 m)

Since ten pieces of baggage are dropped, the total angular momentum of the baggage can be calculated as:

L_total = 10 * L_baggage
= 10 * (16.5 kg * 2.95 m * (ω_initial * 2.95 m))

Finally, using the conservation of angular momentum, we equate the initial angular momentum to the final angular momentum:

L_initial = L_final

I_initial * ω_initial = (I_initial + 10 * (16.5 kg * 2.95 m^2)) * ω_final

Solving for ω_final, we get the final angular speed of the carousel.