Satellite mechanics: linear and rotational momentum

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Homework Help Overview

The discussion revolves around the mechanics of a satellite, specifically focusing on the concepts of linear and rotational momentum. The original poster presents a scenario involving a satellite with a thruster that ejects propellant, raising questions about how the momentum is distributed between linear motion and rotation.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the assumptions necessary to analyze the problem, including the nature of the impulse delivered to the satellite and the conservation laws applicable to the scenario. Questions are raised about the conservation of linear and angular momentum, and the mathematical expressions related to these quantities are discussed.

Discussion Status

There is an ongoing exploration of the concepts involved, with participants providing guidance and prompting the original poster to consider various aspects of the problem. Some participants have posed specific questions aimed at clarifying the original poster's understanding of the relevant physics principles.

Contextual Notes

Participants note that a fundamental understanding of angular momentum and its dependence on the chosen reference point is crucial. There are indications that the original poster may lack some foundational knowledge necessary to fully engage with the discussion.

  • #31
haruspex said:
If you choose an axis on the line of motion of the mass centre then it does not contribute any angular momentum
it does. A rotary one. Moment of inertia*angular velocity
 
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  • #32
vasya said:
it does. A rotary one. Moment of inertia*angular velocity
No, I wrote that the linear motion would not contribute to the angular momentum about that axis.
Please post the details of your calculation that arrives at 1/3 and 2/3.
 
  • #33
*shudder*. I think I see it. 100 kg m/s of linear momentum and 50 kg m2/s of angular momentum from rotation. He is taking the ratio of two quantities which have different units and pretending that the result is a dimensionless two to one ratio.

Naturally, the linear momentum is also 10,000 kg cm/s of linear momentum and 500,000 kg cm2/s of angular momentum from rotation for an equally defensible one to fifty ratio. "Equally defensible" because neither is at all defensible as a dimensionless ratio.

Two per meter and one per fifty centimeters are both the same ratio. Both have units.
 
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  • #34
jbriggs444 said:
*shudder*. I think I see it. 100 kg m/s of linear momentum and 50 kg m2/s of angular momentum from rotation. He is taking the ratio of two quantities which have different units and pretending that the result is a dimensionless two to one ratio.

Naturally, the linear momentum is also 10,000 kg cm/s of linear momentum and 500,000 kg cm2/s of angular momentum from rotation for an equally defensible one to fifty ratio. "Equally defensible" because neither is at all defensible as a dimensionless ratio.

One half per meter and one per fifty centimeters are both the same ratio. Both have units.
Yes, that's probably the blunder. I was thrown by
vasya said:
angular momentum in linear … motion
taking that mean the linear momentum's contribution to angular momentum.
 
  • #35
jbriggs444 said:
An expanding plume of rocket exhaust of unknown mass and velocity that has 100 kg m/s of linear momentum at an offset of 0.5 meters from the craft's center of mass for a total of -50 kg m2/s.
look more closely on first picture in this thread. thruster has offset of 0.25m of y-piersing-through-the-center-of-mass axis
 
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  • #36
vasya said:
look more closely on first picture in this thread. thruster has offset of 0.25m of y-piersing-through-the-center-of-mass axis
Thank you. That explains the factor of two discrepancy in our two evaluations for rotation rate.
 

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