What is the moment of inertia of a thin rod of length L about an axis perpendicu

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Question: What is the moment of inertia of a thin rod of length L about an axis perpendicular to it and passing through its center?

Options:

Correct Answer: (1/12)ML^2

Solution:

The moment of inertia of a thin rod about an axis through its center is given by I = (1/12)ML^2.

What is the moment of inertia of a thin rod of length L about an axis perpendicular to it and passing through its center?

What is the moment of inertia of a thin rod of length L about an axis perpendicular to it and passing through its center?

Correct Answer: I = (1/12)ML^2

Step 1: Understand what moment of inertia means. It is a measure of how difficult it is to change the rotation of an object.
Step 2: Identify the shape of the object. In this case, we have a thin rod.
Step 3: Know the length of the rod, which is given as L.
Step 4: Recognize that the axis of rotation is perpendicular to the rod and passes through its center.
Step 5: Use the formula for the moment of inertia of a thin rod about an axis through its center, which is I = (1/12)ML^2.
Step 6: In the formula, M represents the mass of the rod, and L is the length of the rod.

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