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2010•Journal of Henan Polytechnic UniversityRequires access

A diagrammatic method to determine moment and product of inertia

Yuan-lue Li

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Abstract

Tensor was used to analyze the moment and product of inertia of a plane figure on coordinate axes and the correspondence of principal axes and principal moment of inertia.A diagrammatic method was proposed to solve the above problems.The results show that the moment and the product of inertia of a plane figure on any pair of orthogonal axes are mutual restraints and change in a circle,and the coordinates of the points of the circle are the moment and the product of inertia,which can be used to determine the principal axis position and moment of inertia.The method is more intuitive and simple,and is a supplement to the transformation equation of the moment and product of inertia.

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What this paper is about

Tensor was used to analyze the moment and product of inertia of a plane figure on coordinate axes and the correspondence of principal axes and principal moment of inertia.A diagrammatic method was proposed to solve the above problems.The results show that the moment and the product of inertia of a plane figure on any pair of orthogonal axes are mutual restraints and change in a circle,and the coordinates of the points of the circle are the moment and the product of inertia,which can be used to determine the principal axis position and moment of inertia.The method is more intuitive and simple,and is a supplement to the transformation equation of the moment and product of inertia.

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Available abstract

Tensor was used to analyze the moment and product of inertia of a plane figure on coordinate axes and the correspondence of principal axes and principal moment of inertia.A diagrammatic method was proposed to solve the above problems.The results show that the moment and the product of inertia of a plane figure on any pair of orthogonal axes are mutual restraints and change in a circle,and the coordinates of the points of the circle are the moment and the product of inertia,which can be used to determine the principal axis position and moment of inertia.The method is more intuitive and simple,and is a supplement to the transformation equation of the moment and product of inertia.

Key concepts: Moment of inertia, Euler's equations, Principal axis theorem, Diagrammatic reasoning, Moment (physics), Mathematics, Inertia, Position (finance)

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