An Investigation into the Moment of Inertia of a Hollow, Cylindrical Rod

Abstract

This paper presents an experimental determination of the moment of inertia of a hollow cylindrical rod using a bifilar pendulum. The bifilar pendulum is a torsional oscillation system in which a rigid body is suspended by two parallel strings, allowing rotational inertia to be extracted from the dynamics of its oscillation. The period of torsional oscillation T was measured across eight values of string separation r (0.10 m to 0.45 m), with all other parameters held constant. The theoretical relationship T = (2π/r)√(IL/mg) predicts an inverse proportionality between T and r, confirmed experimentally by a power-law fit with R² = 0.9952. Linearisation of T versus 1/r yielded a best-fit gradient of 0.6206 m·s (R² = 0.9988), from which the moment of inertia was derived as I = (2.01 ± 0.063) × 10⁻² kg·m². The bifilar pendulum method determines rotational inertia without requiring knowledge of the object's internal geometry, making it applicable to objects of complex or unknown shape. This is particularly advantageous for hollow or geometrically irregular objects where direct calculation of rotational inertia from physical dimensions alone is impractical. Sources of systematic error including elliptical motion, manual timing, and string friction are evaluated quantitatively. A theoretical comparison reveals a discrepancy between the experimental and predicted values, attributed primarily to non-purely-torsional motion during oscillation, which is discussed in the context of the method's limitations and directions for future refinement.