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The moment of inertia, denoted by I, measures the extent to which an object resists rotational acceleration about a particular axis; it is the rotational analogue to mass (which determines an object's resistance to linear acceleration). The moments of inertia of a mass have units of dimension ML 2 ([mass] × [length] 2).
Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics , and described by Isaac Newton in his first law of motion (also known as The Principle of Inertia). [ 1 ]
Moments of inertia may be expressed in units of kilogram metre squared (kg·m 2) in SI units and pound-foot-second squared (lbf·ft·s 2) in imperial or US units. The moment of inertia plays the role in rotational kinetics that mass (inertia) plays in linear kinetics—both characterize the resistance of a body to changes in its motion. The ...
the electronvolt (eV), a unit of energy, used to express mass in units of eV/c 2 through mass–energy equivalence; the dalton (Da), equal to 1/12 of the mass of a free carbon-12 atom, approximately 1.66 × 10 −27 kg. [note 2] Outside the SI system, other units of mass include: the slug (sl), an Imperial unit of mass (about 14.6 kg)
The reduced mass is always less than or equal to the mass of each body: , and has the reciprocal additive property: = + which by re-arrangement is equivalent to half of the harmonic mean. In the special case that m 1 = m 2 {\displaystyle m_{1}=m_{2}} : μ = m 1 2 = m 2 2 {\displaystyle \mu ={\frac {m_{1}}{2}}={\frac {m_{2}}{2}}}
Radius of gyration (in polymer science)(, unit: nm or SI unit: m): For a macromolecule composed of mass elements, of masses , =1,2,…,, located at fixed distances from the centre of mass, the radius of gyration is the square-root of the mass average of over all mass elements, i.e.,
In SI units, mass is measured in kilograms, speed in metres per second, and the resulting kinetic energy is in joules. For example, one would calculate the kinetic energy of an 80 kg mass (about 180 lbs) traveling at 18 metres per second (about 40 mph, or 65 km/h) as
They noted that the unit of length in this system is the radius of the first Bohr orbit and their velocity is the electron velocity in Bohr's model of the first orbit. In 1959, Shull and Hall [4] advocated atomic units based on Hartree's model but again chose to use as the defining unit.