Question

In the diagram shown below all three rods are of equal length $L$ and equal mass $M$. The system is rotated such that rod $B$ is the axis. What is the moment of inertia of the system?

• A. $\frac{ML^{2}}{6}$
• B. $\frac{4}{3}ML^{2}$
• C. $\frac{ML^{2}}{3}$
• D. $\frac{2}{3}ML^{2}$

Answer 1

Answer: (A)

$\frac{ML^{2}}{6}$

Answer 2

Since the width is negligible, the moment of inertia of B is zero along its length. $I_{A}+I_{C}=\frac{mL^{2}}{12}+\frac{mL^{2}}{12}-\frac{mL^{2}}{6}$