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The problem describes a cube rotating about an axis passing through its center and the center of one of its faces. It compares the moment of inertia in this situation to that of the previous activity, where presumably the axis of rotation was different, possibly through an edge or a corner.

### Qualitative Explanation:
The **moment of inertia** measures how difficult it is to rotate an object around a given axis. It depends on the distribution of the object's mass relative to the axis. The **parallel axis theorem** helps in calculating the moment of inertia when an object is rotated about an axis that does not pass through its center of mass.

In this scenario:
- When the cube rotates about an axis passing through its center and the center of one of its faces, the mass distribution is more evenly spread around the axis. The distances of the cube's mass elements from the axis are relatively small.
- In contrast, if the axis in the previous activity passed through a corner or edge, the mass elements would be, on average, farther from the axis. According to the formula for moment of inertia \( I = \sum m r^2 \) (where \( r \) is the distance from the axis), the greater distances lead to a higher moment of inertia.

Thus, the moment of inertia is smaller when the axis passes through the center and face because the cube’s mass is closer to the axis. The **parallel axis theorem** supports this by showing that moving the axis farther from the center of mass increases the moment of inertia.

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### Related Questions:
1. What is the exact formula for the parallel axis theorem?
2. How does moment of inertia change for different shapes like spheres or cylinders?
3. How does mass distribution affect rotational motion?
4. How can the center of mass impact the rotational stability of an object?
5. What are other common real-life applications of the parallel axis theorem?

### Tip:
When dealing with rotational dynamics, always check the relative distance of mass from the axis of rotation—this greatly influences the moment of inertia and thus the difficulty of rotating the object.

The cube from the previous activity is instead rotating about an axis passing through its center (and through the center of one of its faces). The parallel axis theorem can be used to demonstrate that the moment of inertia about this axis is smaller than the moment of inertia about the axis in the previous activity. Give a qualitative explanation accounting for this result.

Understand how to calculate the moment of inertia of a cube rotating about an axis passing through its center and face, and why it is smaller compared to other axes using the parallel axis theorem. This explanation involves rotational dynamics, mass distribution, and the parallel axis theorem. Ideal for undergraduate physics students.

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