To solve the problem in the image, we need to address the shift in the rotation point using the parallel axis theorem, which states:

$I = I_{\text{CM}} + Md^2$

Where:

• $I$ is the moment of inertia about the new axis.
• $I_{\text{CM}}$ is the moment of inertia about the center of mass.
• $M$ is the mass of the rod.
• $d$ is the distance between the new axis of rotation and the center of mass.

Steps to Solve:

1. Identify the moment of inertia at the center of mass for a thin rod. This is given by: $I_{\text{CM}} = \frac{1}{12} M L^2$ where $L$ is the length of the rod.

2. Determine the distance $d$ from the center of mass to the new axis of rotation, as specified in the question.

3. Substitute $I_{\text{CM}}$, $M$, and $d$ into the parallel axis theorem formula.

Let me know if you’d like me to calculate with specific values or clarify any part of the solution!

Follow-up Questions:

1. What specific values of $M$, $L$, and $d$ should be used to calculate the new moment of inertia?
2. Would you like to see a derivation of the parallel axis theorem?
3. How does the mass distribution along the length of the rod affect these calculations?
4. Would you like an explanation of how this applies to real-world scenarios like pendulums?
5. Should we explore how this result changes for other geometrical objects?

Tip: Always visualize the axis of rotation and the distances involved when applying the parallel axis theorem.