Conservation of spin, energy and momentum

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Discussion Overview

The discussion revolves around the conservation of spin, energy, and momentum in the context of a person jumping onto a merry-go-round (MGR). Participants explore the definitions of isolated systems, the effects of external forces, and the implications for angular momentum, linear momentum, and energy conservation during inelastic collisions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants express confusion about when a system is considered isolated, particularly in relation to external forces affecting momentum.
  • There is a discussion about whether linear momentum is conserved when a person jumps onto the MGR, with some arguing it is not conserved due to external forces acting on the system.
  • Participants debate the conservation of energy, with some suggesting that energy is not conserved due to friction during the collision, while others propose that mechanical energy is lost in inelastic collisions.
  • Angular momentum is discussed, with some participants asserting that it is conserved because there is no external net torque acting on the person-MGR system.
  • Questions arise regarding the treatment of forces from the MGR's axis and whether they are considered external or internal to the system.
  • Some participants propose expanding the system to include the axis, ground, and Earth, questioning whether this would eliminate external forces.
  • There is a discussion about the nature of energy loss in inelastic versus elastic collisions, with participants exploring the reasons behind energy dissipation and the conditions under which collisions can be considered elastic.

Areas of Agreement / Disagreement

Participants do not reach a consensus on several points, particularly regarding the conservation of linear momentum and energy in inelastic collisions. Multiple competing views remain on the definitions of isolated systems and the treatment of forces acting on the system.

Contextual Notes

Participants highlight limitations in their understanding of the definitions of isolated systems, the role of friction, and the conditions under which energy is conserved or lost. There is also uncertainty about the implications of including various components in the system.

  • #31
Doc Al said:
OK. That's certainly possible for an elastic collision. It's not the scenario we've been discussing, but OK.


Yes, you can represent the person's angular momentum and angular velocity by vectors.

I don't understand. Relative to what?

Seems like you're trying to say that angular velocities can be represented by vectors. OK.


To find the angular momenta, multiply the angular velocity by the rotational inertia, not the mass.

Huh??
There was a slip. It should read as relative angular velocity and not relative velocity. Relative angular velocity = (angular velocity of the person - angular velocity of MGR)
Relative angular velocity is the angular velocity of the person relative to the angular velocity of MGR.

I stand corrected. You are right. To find the angular momenta, we must multiply the angular velocity by the rotational inertia, not the mass.
 

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