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Document Title
Fundamentals of Stress and Vibration Chapter Title
[A Practical guide for aspiring Designers / Analysts] 2. Engineering Mechanics
2.6.2 Parallel and Perpendicular axis theorem
The axes of rotation need not always pass through the CG. For example, the axis of rotation for a
compound pendulum, shown in [Fig 2.34], is through the pivot, and hence, we need mass
moment of inertia about an axis through the pivot.
[Fig 2.34: Compound pendulum oscillating about a pivot]
Parallel axis theorem: This situation, could be tackled using parallel axis theorem instead of
integrating for the entire length, assuming that I CG is known.
The mass moment of inertia of the compound pendulum about the pivot axis is given by:
2
I pivot = I CG + m mass of the compound pendulum ∗ d
This approach of evaluating MMOI about an axis parallel to the CG axis is called “parallel axis
theorem”. This theorem could be applied to an assembly of components as well.
Perpendicular axis theorem: when the mass moments of inertia of a component along two
perpendicular axes are known, then, the mass moment of inertia could be computed about the third
perpendicular axis using the perpendicular axis theorem.
Page 46 QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries,
