Satellite mechanics: linear and rotational momentum

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SUMMARY

This discussion focuses on the mechanics of a 100 kg satellite with a thruster that ejects 100 g of propellant at 1000 m/s, generating a total momentum of 100 kg m/s. Participants analyze how this momentum is distributed between linear and rotational motion, emphasizing the conservation of linear and angular momentum. Key equations discussed include the definitions of angular momentum and kinetic energy, with specific attention to the moment of inertia for a cube. The conversation highlights the complexities of momentum transfer during rapid ejection events and the implications for energy conservation.

PREREQUISITES
  • Understanding of classical mechanics principles, including linear and angular momentum.
  • Familiarity with the equations of motion, specifically F=ma and its implications for momentum.
  • Knowledge of torque and angular acceleration, including their relationship to angular momentum.
  • Basic understanding of moment of inertia calculations for rigid bodies.
NEXT STEPS
  • Study the conservation laws of linear and angular momentum in detail.
  • Learn about the moment of inertia for various shapes and how it affects rotational dynamics.
  • Explore the implications of impulse and momentum transfer in rocket propulsion systems.
  • Investigate the differences in energy transfer when thrusters are positioned at different points on a body.
USEFUL FOR

Students and professionals in physics, aerospace engineering, and mechanical engineering who are interested in satellite dynamics and the principles of momentum in mechanical systems.

  • #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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