The moment of inertia is a measure of an object's resistance to rotational motion. For a square plate, the moments of inertia about different axes can be compared. When considering the moment of inertia about a diagonal (I_d) and about a side in its plane (I_s), the relationship between these two can be understood through the parallel axis theorem and the geometry of the square.
Key Relationships
For a square plate, the moment of inertia about a side (I_s) is typically greater than the moment of inertia about a diagonal (I_d). This is because the mass distribution relative to the axis of rotation is more concentrated when rotating about a side compared to a diagonal.
Conclusion on the Comparison
- I_s > I_d is the correct relationship.
Thus, the answer is C) I_s > I_d.