Is spin angular momentum increasing in a gyroscope?

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SUMMARY

The discussion centers on the precession frequency of a gyroscope, defined by the equation Ω = τ/Iω. Participants clarify that angular momentum is conserved, implying it cannot increase without external torque. The moment of inertia may vary if the gyroscope's shape changes, but overall angular momentum remains constant or decreases due to friction. This highlights the importance of understanding the relationship between torque, moment of inertia, and angular momentum in gyroscopic motion.

PREREQUISITES
  • Understanding of angular momentum conservation principles
  • Familiarity with gyroscopic motion and precession
  • Knowledge of torque and its effects on rotational dynamics
  • Basic grasp of moment of inertia and its dependence on shape
NEXT STEPS
  • Study the derivation of the precession frequency equation Ω = τ/Iω
  • Explore the effects of external torque on angular momentum
  • Investigate the relationship between moment of inertia and shape changes in gyroscopes
  • Learn about frictional forces and their impact on angular momentum in rotating systems
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the dynamics of rotating systems and gyroscopic motion.

applestrudle
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In my textbook there is an equation for the precession frequency:

Ω = τ/Iω

The derivation in the book shows no difference in the spin angular momentum at time t = 0 and t = delta t but when I tried it I got that the denominator of the above equation must be the 'new' angular momentum (at t = delta t)

If the spin angular momentum is increasing with time wouldn't that means the precession frequency would be decreasing but my textbook says constant velocity

:confused:
 
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I'm not sure what you are asking, but angular momentum is conserved, so it can't increase without some external torque. The moment of inertia could change if the gyroscope changes shape, but the angular momentum should stay constant, or be slowly decreasing due to friction.
 

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