Consider a wooden beam used in construction, having a length 𝐿 and a uniform mass 𝑀. This beam is suspended horizontally, with an axis of rotation passing through its midpoint and perpendicular to its length. Derive the formula for the moment of inertia of the beam about this central axis.

• A. $\frac{1}{3} M L^{2}$
• B. $\frac{1}{4} M L^{2}$
• C. $\frac{1}{6} M L^{2}$
• D. $\frac{1}{12} M L^{2}$

Answer: (D)