How Do You Calculate Angular Velocity and Moment of Inertia?

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SUMMARY

The discussion focuses on calculating angular velocity and moment of inertia in a system involving two bars collapsing towards a central axis of symmetry. Ed highlights the importance of considering both rotational kinetic energy and translational kinetic energy due to the motion of the center of mass of the bars. The calculations for moment of inertia (I) are critical for determining angular velocity in this scenario. Participants are encouraged to review their working to ensure all kinetic energy components are accounted for.

PREREQUISITES
  • Understanding of angular velocity and moment of inertia concepts
  • Familiarity with rotational kinetic energy calculations
  • Knowledge of translational kinetic energy principles
  • Basic principles of mechanics and dynamics
NEXT STEPS
  • Study the equations for calculating moment of inertia for various shapes
  • Learn how to derive angular velocity from moment of inertia
  • Explore the relationship between translational and rotational kinetic energy
  • Investigate the dynamics of systems with multiple bodies in motion
USEFUL FOR

Students in physics, mechanical engineers, and anyone studying dynamics and rotational motion will benefit from this discussion.

edeffect
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Hey

Just trying to work out this question (see image). Solving for I (see other image) in an effort to find the angular velocity. Could someone have a look at this working and tell what I am doing right and wrong?

Thanks Heaps

Ed
 

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There is not only going to be rotational kinetic energy, but translational KE as well. After all, the center of masses of both bars are falling and are also moving toward each other, as the system collapses toward the central axis of symmetry.
 

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