Total Angular Momentum of a Tractrix

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SUMMARY

The discussion focuses on calculating the total angular momentum of a 5.0 m tractrix at two different hitchpoint speeds, specifically 60 km/h and 70 km/h. The user observed an unexpected result where the total angular momentum was higher at the lower speed. Key equations mentioned include those for instantaneous angular momentum (L(t)) and the concept of cumulative momentum through impulse (F*t). The user seeks assistance in converting the instantaneous angular momentum equation to reflect total or cumulative momentum.

PREREQUISITES
  • Understanding of angular momentum concepts
  • Familiarity with impulse and Newton's laws of motion
  • Knowledge of calculus for derivatives and equations of motion
  • Experience with tractrix geometry and its applications
NEXT STEPS
  • Research the derivation of cumulative angular momentum equations
  • Study impulse-momentum theorem applications in rotational dynamics
  • Explore numerical methods for solving angular momentum problems
  • Learn about the properties of tractrix curves in physics
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Physics students, mechanical engineers, and anyone involved in dynamics and motion analysis will benefit from this discussion.

Dr Edward
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I have a 5.0 m tractrix and am trying to work out angular momentum and total angular momentum for two hitchpoint speeds 60 & 70 km/h.
My result shows a higher total angular momentum for the lower speed.
This is not what I expected.
Here are my equations
Positions:
View attachment 8589
Derivatives
View attachment 8590
Angular velocity
View attachment 8591
Angular Momentum
View attachment 8592
TOTAL ANGULAR MOMENTUM
View attachment 8593
If anyone can help spot the error I would be extremely grateful
 

Attachments

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  • Derivatives.JPG
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  • Ang Vel.JPG
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  • Ang Momentum.JPG
    Ang Momentum.JPG
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  • Total Mom.JPG
    Total Mom.JPG
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I have spotted the error but don't know how to fix it.
The equation for L(t) is for instantaneous angular momentum.
Momentum is cumulative. i.e. if I add an impulse (F*t) to the classic linear analogy I impart momentum. Newton's 1st law says it will go on forever.
If I now hit it with the same impulse I will double the momentum.
Is there any mathematical genius that will convert the equation for instant angular momentum (L(t)) to total or cumulative momenta.

I should be ever so grateful.
 

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