Representation of Rotating and Translating Body

[MisterDD]

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.

 

[kuruman]

Hi MisterDD and welcome to PF.

Besides energy transfer, you should also consider transfer of linear and angular momentum.

 

[MisterDD]

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)

 

[kuruman]

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.

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