How to Determine θ for a Sliding Block Sticking to a Pivoting Rod?

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SUMMARY

The discussion revolves around determining the angle θ for a 60 g block sliding down a frictionless surface and sticking to a uniform rod of mass 105 g and length 40 cm. The conservation of energy principle is applied to find the angular velocity (ω) of the rod at the moment of impact. The final solution involves using the relationship between initial and final angular momentum (Li=Lf) to calculate the angle θ after the rod pivots and momentarily stops.

PREREQUISITES
  • Understanding of conservation of energy principles
  • Familiarity with angular momentum concepts
  • Knowledge of rotational dynamics
  • Basic mechanics involving frictionless surfaces
NEXT STEPS
  • Study the conservation of angular momentum in detail
  • Learn about rotational motion equations and their applications
  • Explore energy conservation in mechanical systems
  • Investigate the effects of mass and length on pivoting rods
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Students in physics, particularly those studying mechanics, as well as educators and anyone involved in solving problems related to rotational dynamics and energy conservation.

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Homework Statement


In the figure below, a small 60 g block slides down a frictionless surface through height h = 20 cm and then sticks to a uniform rod of mass 105 g and length 40 cm. The rod pivots about point O through angle θ before momentarily stopping. Find θ.
(Picture attached)

Homework Equations


Li=Lf, L=I[omega]


The Attempt at a Solution


I used conservation of energy to find [omega] as the block hits the rod, but I'm not sure if that's right or where to go from there
 

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I finally solved it! Thanks anyway!
 

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