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?

Updated On: Jul 28, 2022
  • $\frac{ML^{2}}{6}$
  • $\frac{4}{3}ML^{2}$
  • $\frac{ML^{2}}{3}$
  • $\frac{2}{3}ML^{2}$
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The Correct Option is A

Solution and Explanation

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

System of Particles and Rotational Motion

  1. The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
  2. The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
  3. The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.