Representation of Rotating and Translating Body

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Discussion Overview

The discussion revolves around the dynamics of a small mass moving in a spiral path and its collision with a larger mass. Participants explore the assumptions necessary to create an equivalent system that only involves linear motion, focusing on energy and momentum transfer during the impact.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that to create an equivalent system with only linear motion, the tip velocity of the small mass at the instant of impact could be considered as the linear velocity of the whole body.
  • Another participant emphasizes the importance of considering both energy transfer and the transfer of linear and angular momentum during the collision.
  • A further contribution clarifies that just before the collision, the small mass can be assumed to be moving in a straight line, with its direction of motion being tangent to the spiral path at the point of contact.
  • It is noted that the collision occurs over a very short time interval, suggesting that external forces affecting the small mass's spiral motion do not significantly influence the energy and momentum transfer during the collision.

Areas of Agreement / Disagreement

Participants express different views on the assumptions needed for the equivalent linear motion system, indicating that multiple competing perspectives remain regarding the dynamics of the collision and the simplifications involved.

Contextual Notes

There are unresolved aspects regarding the exact conditions under which the equivalent system can be accurately defined, particularly concerning the impact of external forces and the assumptions about the motion of the small mass prior to collision.

MisterDD
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Hello Everyone..

Consider a small moving mass following a spiral path away from center and the body is rotating about its center as well. At some time the body impacts with a relatively bigger mass and transfers some of its energy to it. If we want to make an equivalent system with only linear motion, what are the assumptions we need to consider? Actual task is to study the impact of smaller mass on bigger mass. One suggestion from my side is to consider the tip velocity of small mass at the instant of impact as linear velocity of the whole body and orientation as the same time. Is this simplification valid for accurately evaluating dynamics of the system?
Any other comments and suggestions are welcome..
Thanks.
 
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Hi MisterDD and welcome to PF.

Besides energy transfer, you should also consider transfer of linear and angular momentum.
 
kuruman said:
Hi MisterDD and welcome to PF.

Besides energy transfer, you should also consider transfer of linear and angular momentum.
Thank you kuruman.. I was about to correct my question and I saw your reply. Please have a look at it once more.. I need to make an equivalent system with only linear motion (no rotation)
 
Let me understand what you are asking. You have a small mass that is spiraling out and at some point in time it collides with another mass. You want to "make an equivalent system with only linear motion". In what sense is the this latter system equivalent? Note that just before the collision, you can assume that the small mass is moving in a straight line, the direction of motion being tangent to the spiral at the point of contact with the other mass. The fact that the small mass was moving along the spiral earlier bears no relevance to what happens during the collision. So as a result of the collision, you have transfer of energy and linear momentum. If the small mass is spinning, it may also transfer some of its spin to the other mass. The collision may be assumed to take place in a very short time interval dt so that the external force causing the small mass to follow a spiral path does not appreciably affect the energy and momentum of the two-mass system during this short time dt.

Did I answer your question?
 
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