What is Reduced mass: Definition and 25 Discussions

In physics, the reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics. It is a quantity which allows the two-body problem to be solved as if it were a one-body problem. Note, however, that the mass determining the gravitational force is not reduced. In the computation, one mass can be replaced with the reduced mass, if this is compensated by replacing the other mass with the sum of both masses. The reduced mass is frequently denoted by


{\displaystyle \mu }
(mu), although the standard gravitational parameter is also denoted by


{\displaystyle \mu }
(as are a number of other physical quantities). It has the dimensions of mass, and SI unit kg.

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  1. S

    I Reduced mass to bind hyper- and mesonuclei

    A deuteron is a bound hexaquark. Since both triquarks have severally masses of about 940 MeV, the reduced mass of a deuteron is under 470 MeV. Deuteron is bound... but only feebly. It has only one bound state: ground state orthodeuteron. All excited states of orthodeuteron are unbound...
  2. T

    B Reduced mass to atomic mass units conversion help please

    Hello I am trying to understand how to write the reduced mass into atomic mass units but i am confused how it was done. The equation is $$m_1m_2/(m_1+m_2)$$ For two similar masses in my particular case i have: $$m^2 / 2m = 1/2 * m$$ Then to convert to atomic mass units, the book says it...
  3. Arman777

    I Reduced mass for ##m_1## larger than ##m_2##

    Reduced mass can be defined as ##μ= \frac {m_1m_2} {m_1+m_2}## For ##m_1>>m_2##, ##μ_2≈m_2## How can we prove this ?
  4. O

    Energy Lost during elastic collision.

    Homework Statement . True or False:[/B] For a completely elastic collision of two isolated masses the energy lost is ½μνr2 Where μ is the reduced mass of the system and νr is the magnitude of relative velocity between the two particles. Homework EquationsThe Attempt at a Solution Elastic...
  5. K

    I Reduced mass effect on gyromagnetic factor

    Is there an effect of reduced mass on the orbital g factor? In Bethe and Salpeter (1957) Quantum Mechanics of One and Two Electron Atoms p214, it mentions a reduced mass effect on ##g_L = \frac{\mu}{m_e}##. (At least, that's what my notes said. I don't have Bethe and Salpeter in front of me...
  6. S

    Trajectories of planets using reduced mass and CM frame

    In planetary motion, the reduced mass of a system \mu is used in order to study the motion of the planet m in the non-inertial frame of the star M. Using \mu the trajectory of m turns out to be a conic. But this is the trajectory of the planet m as seen from the star M, correct? I read that in...
  7. squelch

    The Bohr Radius and reduced mass

    Homework Statement A muon is a particle with a charge equal to that of an electron and a mass equal to 207 times the mass of an electron. What is the radius and energy of the ground state of hydrogen if the electron is replaced with a muon? Don't forget to use the concept of reduced mass...
  8. AdityaDev

    Why Does the Reduced Mass Concept Yield a Positive Total Energy?

    According to the concept: when a planet revolves around a star, and when both the bodies move in circular orbits due to the interaction between each other, both the bodies can be replaced by a single body of mass ##\mu## revolving in a circular orbit of radius equal to the distance between both...
  9. F

    Can't get my head around reduced mass (particle physics)

    I know it's probably simple but I just don't understand reduced mass. I am trying to work out the reduced mass of 4He+. m = memN / me + mN Can somebody please just explain step by step what I do. This is only a segment of a 1 mark question and I'm getting my knickers in a frustratingly twisty...
  10. Medicol

    Electrolysis and reduced mass of a metal bar

    1. Insert a bar of copper of m(gram) into (HCl + H2O). After a while, its weight become m_1 (gram) which is smaller than m. Explain why and give a general formula to find m_1 2. None 3. I keep thinking how that becomes possible, because I learn that Cu can't react with HCl+H2O
  11. S

    Explore the Concept of Reduced Mass: Examples & Applications

    Homework Statement The Concept of the reduced mass was introduced Homework Equations What is the application for the μ,which we have to learn, in questions like in shm or collision So i was just wondering if you could show me some examples where in the concept of reduced mass has...
  12. D

    Deriving Equation of Reduced Mass W/ Angular Momentum

    Homework Statement Derive m*= mM/(m+M) *hint* total angular momentum Iω=m*r2ω equals the sum of the individual angular momenta, where r = re + rn; re and rn are the distances of the electron and nucleus respectively from the center of mass. Homework Equations Angular Momentum = mvr...
  13. N

    Rethinking Newton's Equation: Re-writing F=MA with Reduced Mass

    I am the president of the Physics club at my high school. One of our members came up with a very interesting hypothetical. He asked each of us to re-write the famous Newtonian equation for motion, F=MA(force equals mass times acceleration). Here's the question we are all trying to answer, if...
  14. K

    Lande' g-Factor: Is a Reduced Mass Correction Needed?

    Ok. The Lande' g-factor is given as g = g_L \frac{J(J+1)-S(S+1)+L(L+1)}{2J(J+1)} + g_s\frac{J(J+1)+S(S+1)-L(L+1)}{2J(J+1)} Most sources say that g_L = 1 exactly, but Bethe and Salpeter p214 seems to indicate that there should be a correction for reduced mass. g_L = 1- \frac{m_e}{m_i} Is...
  15. DiracPool

    Trying to understand reduced mass

    I understand that the reduced mass is used to simplify a two-body problem into a one body problem, so that instead of calculating two masses rotating around a common center as in the Earth and moon, you can treat the Earth as stationary, and then used a "reduced" mass for the moon in the...
  16. S

    Reduced Mass: Origin & Significance

    Will anyone help me to understand the concept of reduced mass , where does it come from and its physical significance
  17. S

    Application/use of reduced mass in conservation of momentum/energy problems

    I want to know in which types of problem this reduced mas μ=m1*m2/(m1+m2) is used . All i know that it is closely related to center of mass of the system but don't know exactly where to use it?
  18. S

    Does the Reduced Mass Trace an Ellipse in a Rotating Two-Body System?

    In a system of two rotating masses about a point (i.e, the sun), would the reduced mass (used for calculations) trace out another ellipse?
  19. B

    Calculating Reduced Mass of NO+ Molecular Ion: Missing Electron Considerations

    Homework Statement I want to calculate the reduced mass of a molecular ion, NO^{+} (singly-ionized nitrogen monoxide molecule) in atomic units. My question is, how would I take into account the missing electron in this calculation. Homework Equations mass of N in a.u. is about 25525...
  20. B

    Calculating Reduced Mass for Schrodinger's Equation

    If the electron of the h-atom is not moving in a classical orbit (like a circular orbit) why is the reduced mass used in Schrodinger's equation?
  21. A

    Calculating Reduced Mass of Molecules

    [SOLVED] reduced mass?! Hi there, I know the reduced mass is defining with the below formula: \frac{1}{\mu} = \frac{1}{m _{1}} + \frac{1}{m_{2}} + ... In Bohr's radius when i want to find the \mu i use the m1 = mass of electron m2 = mass of poroton but what if i need to find...
  22. C

    Reduced mass for an infinite mass and a finite mass?

    Homework Statement We have a collision between a finite mass steel ball and an infinite mass steel wall and must find the maximum compression if we are given the mass of the ball, the initial speed and the constant b (See eq. below). Homework Equations We know that the maximum...
  23. J

    How to Derive the Reduced Mass Formula for Inertia between Two Atoms?

    Does anyone know how to actually derive the reduced mass formula? I have to prove the formula: inertia = (reduced mass)r^2 and am having some difficulties. To be more specific I'm working with the inertia between to atoms where r is the bond length. Any help with this is much...
  24. M

    CM and Relative Coordinates; Reduced Mass

    Two particles of mass m1 and m2 are joined by a massless spring of natural length L and force constant k. Initially, m2 is resting on a table and I am holding m2 vertically above m2 at a height L. At time t=0, I project m2 vertically upward with initial velocity v0. Find the positions of the two...
  25. PeteGt

    Center of mass and REduced mass

    I forget how these two relate both conceptually and mathematically...any help?