Tons of dust and small particles rain down onto the Earth from space every day. As a result, does the Earth's moment of inertia increase, decrease, or stay the same? (b) Choose the best explanation from among the following:

I. The dust adds mass to the Earth and increases its radius slightly.

II. As the dust moves closer to the axis of rotation, the moment of inertia decreases.

III. The moment of inertia is a conserved quantity and cannot change.

Solution 53P

Part (a)

Step 1 of 3:

The Earth gets tons of dust falling from the space every day. We are going to find the change in the moment of inertia of the Earth due to these dust particles.

Step 2 of 3:

The moment of inertia of a body depends on the product of the mass of the object and the square of the distance from the axis of rotation. As the Earth receives dust particles from the space the mass of the Earth obviously increases. It results in the increased moment of inertia.

Answer: The Earth’s moment of inertia increases.

Part (b)