NationMaster - Encyclopedia: Reduced mass

Reduced mass is an algebraic term of the form Algebraic chess notation is the method used today by all competition chess organizations and most books, magazines, and newspapers to record and describe the play of chess games. ...

$x_{red} = {1 over {{1 over x_1} + {1 over x_2}}} = {{x_1 x_2} over {x_1 + x_2}}$

that simplifies an equation of the form

${1over x_{eq}} = sum_{i=1}^n {1over x_i} = {1over x_1} + {1over x_2} + cdots+ {1over x_n}.$

The reduced mass is typically used as a relationship between two system elements in parallel, such as resistors; whether these be in the electrical, thermal, hydraulic, or mechanical domains. This relationship is determined by the physical properties of the elements as well as the continuity equation linking them. An ideal resistor is a component with an electrical resistance that remains constant regardless of the applied voltage or current flowing through the device. ... All the examples of continuity equations below express the same idea; they are all really examples of the same concept. ...

On particular application of the reduced mass is to solve the two-body problem of mechanics as if it were a one body problem. Given two bodies, one with mass $m 1$ and the other with mass $m 2$ , they will orbit the barycenter of the two bodies. The equivalent one-body problem, with the position of one body with respect to the other as the unknown, is that of a single body of inertial mass In classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other. ... Mechanics (Greek ) is the branch of physics concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effect of the bodies on their environment. ... It has been suggested that Center of gravity be merged into this article or section. ... Inertial mass is a measure of the resistance of an entity to a change in its velocity relative to an inertial frame. ...

$m_{red} = {1 over {{1 over m_1} + {1 over m_2}}} = {{m_1 m_2} over {m_1 + m_2}}$

with the force the actual one.

Applying the gravitational formula we get that the position of the first body with respect to the second is governed by the same differential equation as the position of a very small body orbiting a body with a mass equal to the sum of the two masses, because

${{m_1 m_2} over {m_{red}}}=m_1+m_2$ .

The reduced mass is always less than or equal to the mass of each body.

External links

Reduced Mass on HyperPhysics

Categories: Mechanics | Mass

Results from FactBites:

reduced mass: Definition and Much More from Answers.com (226 words)
	Reduced mass is a concept that allows one to solve the two-body problem of mechanics as if it were a one body problem.
	The equivalent one-body problem, with the position of one body with respect to the other as the unknown, is that of a single body of inertial mass
	The reduced mass is always less than or equal to the mass of each body.

The Compton Effect, Newtonian Velocities, The Fundamental Particle (739 words)
	The equivalence is due to conservation of momentum but the scattering and the initial distribution of momentum between "mass" and velocity also identifies a field coupling and a re-established balance between material and anti-material states (electromagnetic and mechanical).
	The sum of the masses of the muon and pion are ½ the mass of the proton divided by the "anomalous" factor in the magnetic moment of the neutron.
	This confirms the "mass defect" of capture (or the energy required for release) is equal to the reduced mass.

More results at FactBites »

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