Reduced Mass: Origin & Significance

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Discussion Overview

The discussion centers around the concept of reduced mass, exploring its origin, significance, and applications in simplifying physical problems, particularly in the context of two-body interactions.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant seeks clarification on the concept of reduced mass and its physical significance.
  • Another participant suggests that reduced mass is primarily a mathematical convenience.
  • A different viewpoint indicates that reduced mass has broader applications beyond mere mathematics, relating it to systems in parallel across various domains.
  • It is noted that reduced mass allows for the simplification of a two-body problem into a one-body problem, leveraging Newton's third law and the concept of the center of mass.
  • Concerns are raised regarding the reliability of Wikipedia as a source for understanding subtle insights related to reduced mass.
  • One participant emphasizes that the relationship between system elements is crucial for the application of reduced mass, suggesting that it relies on specific physical properties.

Areas of Agreement / Disagreement

Participants express differing views on the nature and significance of reduced mass, with some seeing it as a mathematical trick while others argue for its broader implications. The discussion remains unresolved regarding the extent of its significance.

Contextual Notes

Participants highlight the dependence of the concept on the relationships between system elements and the continuity equation, indicating that assumptions about these relationships may affect the understanding of reduced mass.

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

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