Product of Inertia definition of Product of Inertia in the Free Online Encyclopedia.

product of inertia [′prä·dəkt əv i′nər·shə]

(mechanics)

Relative to two rectangular axes, the sum of the products formed by multiplying the mass (or, sometimes, the area) of each element of a figure by the product of the coordinates corresponding to those axes.

Product of inertia

The product of inertia of area A relative to the indicated XY rectangular axes is I_XY = ∫ xy dA (see illustration). The product of inertia of the mass contained in volume V relative to the XY axes is I_XY = ∫ xyρ dV—similarly for I_YZ and I_ZX.

Product of inertia of an area

Relative to principal axes of inertia, the product of inertia of a figure is zero. If a figure is mirror symmetrical about a YZ plane, I_ZX = I_XY = 0. See Moment of inertia

Product of Inertia

a quantity that characterizes the mass distribution in a body or mechanical system. Products of inertia are the sums of the products formed by multiplying the mass m_k of each point of the body or system by the product of two of the coordinates x_k, y_k, z_k of the point

I_xy = ∑ m_kx_ky_k

I_yz = ∑ m_ky_kz_k

I_zx = ∑ m_kz_kx_k

The values of the products of inertia depend on the orientations of the coordinate axes. For every point of the body or system, there exist at least three mutually perpendicular axes, called the principal axes of inertia, for which the products of inertia are equal to zero.

The concept of the product of inertia plays an important role in the study of the rotational motion of bodies. The magnitudes of the pressure forces on the bearings on which the axial shaft of a body rotates depend on the values of the products of inertia. The pressures will be minimal—that is, equal to the static pressures—if the axis of rotation is a principal axis of inertia that passes through the center of mass of the body.

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No references found	Possibly a too cautious pragmatism, the product of inertia, impedes my ready acceptance" Indeed. Of white heroes and old men talking (racists refuse to accept ... by Alfred, Taiaiake / Wind Speaker	prodrug Producer producer gas producer goods producer's risk Producers Producers Cooperative producing gas-oil ratio producing horizon producing reserves Producing Suite product product bundle product data product demodulator product design product detector product information notes product key product liability product life-cycle product line product measure product model product modulator Product of Inertia Product of Labor Product quality product reengineering product research product rule product topology Product usability product water product-moment coefficient Productida Productinida Production Production Art Production Assets Production Assets, Agricultural Production Assets, Fixed Production Association Production Brigade Production Capacity Production Conference Production Contract production control Production Costs Production Cycle production database	Product Markup Language Product Maturity Test Product measure product mix Product Mixes product model Product Model Exchange Using STEP Product Model Query Language Product Modification Request product modulator Product Moment Correlation Product moment correlation coefficient Product moment correlation coefficient Product Name Product Number 03 Product Objective & Requirements Product of Ambulatory Surgery Product of an Act of Making Product of Boredom Product of Combustion Product of Conception Product of Desire Product of Dirichlet Process Mixtures Approach Product of Gene 12 Product of group Product of Inertia Product of Labor Product Of My Environment Product of sums product of the imagination Product of the Year Product of Theft Product of Theft Product Office, Standard Army Maintenance System Product Ontwerpen 4 Product Operator formalism in Mathematica Product Orderability Matrix Product Performance Agreement Center Product Performance Issue Product Performance Qualification Product Performance Specification Product placement Product placement Product Planning & Development Product Planning Process Product Platform Validation Product plug Product Portfolio Management Product Positioning Time Product Price Place Promotion Product Price Variance Product Process Management

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Possibly a too cautious pragmatism, the product of inertia, impedes my ready acceptance" Indeed.

Of white heroes and old men talking (racists refuse to accept ... by Alfred, Taiaiake / Wind Speaker

Product Markup Language
Product Maturity Test
Product measure
product mix
Product Mixes
product model
Product Model Exchange Using STEP
Product Model Query Language
Product Modification Request
product modulator
Product Moment Correlation
Product moment correlation coefficient
Product moment correlation coefficient
Product Name
Product Number 03
Product Objective & Requirements
Product of Ambulatory Surgery
Product of an Act of Making
Product of Boredom
Product of Combustion
Product of Conception
Product of Desire
Product of Dirichlet Process Mixtures Approach
Product of Gene 12
Product of group

Product of Inertia

Product of Labor
Product Of My Environment
Product of sums
product of the imagination
Product of the Year
Product of Theft
Product of Theft
Product Office, Standard Army Maintenance System
Product Ontwerpen 4
Product Operator formalism in Mathematica
Product Orderability Matrix
Product Performance Agreement Center
Product Performance Issue
Product Performance Qualification
Product Performance Specification
Product placement
Product placement
Product Planning & Development
Product Planning Process
Product Platform Validation
Product plug
Product Portfolio Management
Product Positioning Time
Product Price Place Promotion
Product Price Variance
Product Process Management