Angular momentum with a large wooden turntable

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SUMMARY

The discussion centers on the principles of angular momentum and kinetic energy conservation in a system involving a large wooden turntable. Key equations include the conservation of angular momentum (Li = Lf) and the kinetic energy formula (K = (1/2)*(I)*(omega)^2). A common misconception is addressed: while angular momentum is conserved, kinetic energy may not be conserved in inelastic collisions, as illustrated by comparing a clay collision to a parachutist landing on a rotating disk. The conclusion emphasizes the importance of distinguishing between elastic and inelastic collisions in analyzing energy transformations.

PREREQUISITES
  • Understanding of angular momentum (Li = Lf)
  • Familiarity with kinetic energy equations (K = (1/2)*(I)*(omega)^2)
  • Knowledge of elastic vs. inelastic collisions
  • Basic principles of rotational dynamics
NEXT STEPS
  • Study the concept of inelastic collisions and energy loss
  • Learn about the conservation of angular momentum in various systems
  • Explore the effects of external forces on rotational motion
  • Investigate real-world applications of angular momentum in engineering
USEFUL FOR

Students studying physics, educators teaching mechanics, and anyone interested in understanding the principles of angular momentum and energy conservation in rotational systems.

MITPhysics
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Homework Statement



OQzBjfH.png


Homework Equations



Li = Lf
L = I*omega
K = (1/2)*(I)*(omega)^2

The Attempt at a Solution



dXqQxEV.jpg

[/B]
Given that there are no non-conservative forces in action, I am assuming that the two kinetic energies should be equal. However, as shown by my work above, the two values are different, and I do not know where I went wrong.
 

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MITPhysics said:
Given that there are no non-conservative forces in action, I am assuming that the two kinetic energies should be equal.
This is not correct. Compare with the case of a clump of clay with some velovity hitting another stationaty piece of clay and sticking together. Is the kinetic energy the same before and after?
 
How would you describe the collision between the parachutist and the rotating disk?
 

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