What happens to the moment of inertia of a rigid body if it is rotated about an

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Question: What happens to the moment of inertia of a rigid body if it is rotated about an axis that is not its principal axis?

Options:

Correct Answer: It increases

Solution:

The moment of inertia can change when rotating about an axis that is not a principal axis due to the distribution of mass relative to the new axis.

What happens to the moment of inertia of a rigid body if it is rotated about an axis that is not its principal axis?

What happens to the moment of inertia of a rigid body if it is rotated about an axis that is not its principal axis?

Step 1: Understand what moment of inertia is. It is a measure of how difficult it is to change the rotation of an object.
Step 2: Identify what a principal axis is. A principal axis is an axis about which the moment of inertia is calculated and is usually aligned with the object's symmetry.
Step 3: Recognize that when an object rotates about a principal axis, its mass is distributed evenly relative to that axis.
Step 4: When the object rotates about a different axis (not a principal axis), the distribution of mass changes relative to this new axis.
Step 5: Understand that this change in mass distribution affects the moment of inertia, making it different from the moment of inertia calculated about the principal axis.

Moment of Inertia – The moment of inertia is a measure of an object's resistance to rotational motion about a given axis, depending on the mass distribution relative to that axis.
Principal Axis – A principal axis is an axis about which the moment of inertia is minimized, and the distribution of mass is such that the object rotates most efficiently.
Parallel Axis Theorem – This theorem states that the moment of inertia about any axis parallel to a principal axis can be calculated by adding the moment of inertia about the principal axis and the product of the mass and the square of the distance between the two axes.