Conservation of linear momentum in this system

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Discussion Overview

The discussion revolves around the conservation of linear momentum in a system consisting of a mouse on a stationary turntable supported by a frictionless axle. Participants explore whether the momentum of the system remains constant as the mouse begins to walk north on the turntable.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asserts that the initial momentum of the system is zero, as both the mouse and turntable are at rest, but questions the presence of an external net force that would cause a change in momentum when the mouse starts moving.
  • Another participant suggests that the axle exerts an external force on the turntable, allowing it to remain stationary while the mouse moves.
  • A later reply discusses the implications of including the axle as part of the system, proposing that if the axle has finite mass, it would also move, keeping the net linear momentum of the system at zero.
  • Another viewpoint posits that if the axle has infinite mass, it acts as an infinite momentum sink, complicating the calculation of momentum.
  • One participant encourages identifying the forces acting on the axle and applying Newton's laws to further analyze the situation.

Areas of Agreement / Disagreement

Participants express differing views on the role of the axle and the nature of external forces in the system, indicating that multiple competing perspectives remain without consensus.

Contextual Notes

The discussion highlights the dependence on the definitions of the system's boundaries and the assumptions regarding the mass of the axle, which are not resolved.

undividable
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A pet mouse sleeps near the eastern edge of a stationary, horizontal turntable that is supported by a frictionless,
vertical axle through its center. The mouse wakes up and starts to walk north on the turntable. Is the momentum of the system constant?
i understand that the initial momentum is zero, because the turntable and the mouse have v=0, and that the final momentum is not zero, since v≠0 for the mouse, and v=0 for the turntable, so linear momentum is not conserved, but since ∫∑Fext dt=dp, where is the external netforce (∑Fext) that causes the change in the system's momentum? It seems to me there are none. only internal forces (friction) between the mouse and the turntable
 
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undividable said:
where is the external netforce (∑Fext) that causes the change in the system's momentum
The axle
 
Dale said:
The axle

so, as the mouse moves upward, the axle exerts and external force (normal downward force) on the turntable so it stays with v=0? and if the axle was a part of the system? the linear momentum should still change, but now the external net force would be is 0
 
undividable said:
so, as the mouse moves upward, the axle exerts and external force (normal downward force) on the turntable so it stays with v=0? and if the axle was a part of the system? the linear momentum should still change, but now the external net force would be is 0
If the axle has finite mass, it will move south along with the wheel while the mouse moves north. Net linear momentum of the system (including axle) remains zero.

If the axle has infinite mass, it is an infinite momentum sink. Its momentum cannot be calculated by measuring zero velocity and crying "Eureka: zero momentum".
 
undividable said:
and if the axle was a part of the system?
Then identify the forces acting on the axle and apply Newton's laws.
 

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