Conservation of Momentum in Collisions: Exploring Linear and Angular Momentum

In summary, the conversation discusses the conservation of linear and angular momentum in an elastic collision between two balls with different lengths of spokes attached to them. It is explained that according to the conservation of momentum, total momentum is always conserved but angular and linear momentum can be converted between each other. However, it is clarified that they are conserved individually. A specific scenario is presented and the equations for kinetic energy and angular momentum are used to demonstrate that they are both conserved in the collision. The concept of angular momentum being conserved around a specific axis is also explained.
  • #106
jbriggs444 said:
My approach to problem solving is to simplify, simplify, simplify.
An approach that I endorse also.
 
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  • #107
bobie said:
This example is not appropriate, because the body is already moving, and you are not increasing its speed or KE (same applies to orbits, etc.).
This objection is not appropriate, because the spinning gyro is also already moving, and a torque perpendicular to its angular velocity doesn't increase its KE. Just like a force perpendicular to linear velocity doesn't increase KE.

bobie said:
if an object is rotating in one plane it has k KE, if you make it rotate in 2 different planes it has undeniably KE > k, somebody must have given it some KE and therefore must have spent some energy. Is that vague to you? Is this wrong or arguable in any case?
Yes it is wrong. In particular the "undeniably" & "must" part.
 
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  • #108
Since this thread is getting a little tense, and has already gone over 100 posts, the other mentors and I have decided that it is past time to close it.

Bobie, please look at the great advice that you have received from many people and try to actually work out some of the details on the very simplest possible scenarios. Don't assume that you know the answer until you have actually worked out the math.
 

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