Explanation:
If an object has a moment of inertia I₀ about an axis, then the moment of inertia about a different, parallel axis is I = I₀ + md², where d is the distance between the axes.
For example, consider a horizontal thin rod rotating about a vertical axis passing through its center. It has mass m and length L. Its moment of inertia is known to be I = 1/12 mL².
Now consider the same rod, but this time we move the axis of rotation L/2 to the end of the rod. We can use parallel axis theorem to find the new moment of inertia:
I = I₀ + md²
I = 1/12 mL² + m (L/2)²
I = 1/12 mL² + 1/4 mL²
I = 1/3 mL²
