Reduced Mass: Origin & Significance

In summary, reduced mass is a concept used in physics to simplify the calculation of a 2-body problem into a 1-body problem. It is typically used in parallel systems with elements that are related, such as resistors. This relationship is determined by the physical properties and continuity equation of the elements. It allows for the use of Newton's 3rd law to solve for the motion of one body around the center of mass. Ultimately, reduced mass is a trick used to make mathematical calculations easier in these types of systems.
  • #1
Shan K
73
0
Will anyone help me to understand the concept of reduced mass , where does it come from and its physical significance
 
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  • #3
The last two sentences in the Wikipedia article seems to suggest that it can be more than just a math trick.

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.
 
  • #4
It is used to reduce a 2-body problem into a 1-body problem. Newton's 3rd law (equivalent to conservation of momentum) tells us that if two bodies act upon each other, they will both orbit the center of mass of the system, and the two trajectories will be similar (in the geometric sense). So, you only have to solve for the motion of one body around the center of mass. Reduced mass is a trick used to do this.
 
  • #5
And wikipedia is such a reliable source of subtle insights?

The relationship mentioned in wikipedia is what makes the trick work.
If the elements were not related, then it wouldn't work.
 

1. What is reduced mass?

Reduced mass is a concept used in physics to describe the effective mass of a system composed of two or more particles. It is the mass that appears in the equations of motion for the system, and is typically different from the individual masses of the particles.

2. How is reduced mass calculated?

The reduced mass is calculated by taking the reciprocal of the sum of the reciprocals of the individual masses. In mathematical terms, it is expressed as 1/((1/m1)+(1/m2)+...+(1/mn)).

3. What is the significance of reduced mass?

Reduced mass is significant because it allows us to simplify the equations of motion for a system of particles, making calculations easier. It also helps us understand how the masses of individual particles affect the overall motion of the system.

4. What is the origin of reduced mass?

The concept of reduced mass was first introduced by Isaac Newton in his laws of motion. It was later developed further by physicists such as Joseph Louis Lagrange and William Rowan Hamilton.

5. How is reduced mass used in real-world applications?

Reduced mass is used in various fields of physics, such as quantum mechanics, astrophysics, and molecular dynamics, to describe the motion and interactions of particles in a system. It is also used in engineering to calculate the resonant frequency of systems, such as musical instruments and bridges.

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