moment of inertia

English

Noun

moment of inertia (plural moments of inertia)

1. (physics, classical mechanics) A measure of a rigid body's resistance to change in its angular velocity around a given axis.

   The moment of inertia of a rigid body is a quantity that determines the torque needed for a given angular acceleration about a given rotational axis, analogous to how mass determines the force needed for a given acceleration.

   • 1882, Edward John Routh, The Elementary Part of a Treatise on the Dynamics of a System of Rigid Bodies, 4th edition, MacMillan & Co., page 10:

     The moments of inertia of a heterogeneous body whose boundary is a surface of uniform density may sometimes be found by the method of differentiation.

   • 1884, Benjamin Williamson, An Elementary Treatise on the Integral Calculus, 4th edition, Appleton and Company, page 292:

     Consequently, the moment of inertia of a body relative to any axis can be found when that for the parallel axis through its centre of gravity is known.

2. (engineering, structural engineering) Second moment of area; a measure of a rigid body's resistance to bending.
   • 2007, Robert L. Mott, Applied Strength of Materials, 5th edition, Taylor & Francis (CRC Press), page 323:

     Stresses due to vertical shearing forces also depend on moment of inertia and are discussed in Chapter 8.
     Some mathematicians and stress analysts use the term second moment of area instead of moment of inertia. That term is, in fact, more descriptive of the definition of this property in the following discussion.

Synonyms

• (measure of resistance to change in angular velocity): mass moment of inertia, angular mass, rotational inertia
• (measure of resistance to bending): area moment of inertia, second area moment, second moment of area, second moment of inertia

Derived terms

• polar moment of inertia (resistance to torsion)

Related terms

• moment
• moment of force

Translations

measure of resistance to change in angular velocity

• Czech: moment setrvačnosti m
• Danish: inertimoment n
• Finnish: hitausmomentti (fi), inertiamomentti
• French: please add this translation if you can
• German: Trägheitsmoment (de) n, Massenträgheitsmoment n, Inertialmoment n
• Greek: ροπή αδράνειας f (ropí adráneias)
• Indonesian: momen inersia (id)
• Italian: momento di inerzia m
• Portuguese: momento de inércia m
• Romanian: moment de inerție (ro) n
• Russian: моме́нт ине́рции (ru) m (momént inɛ́rcii)

second moment of area — see second moment of area

See also

• planar second moment of area
• second polar moment of area (= polar moment of inertia)

Further reading

• Moment (physics) on Wikipedia.Wikipedia
• List of moments of inertia on Wikipedia.Wikipedia
• List of second moments of area on Wikipedia.Wikipedia
• Parallel axis theorem on Wikipedia.Wikipedia
• Perpendicular axis theorem on Wikipedia.Wikipedia
• Stretch rule on Wikipedia.Wikipedia
• Rigid body dynamics on Wikipedia.Wikipedia