[Rotational Inertia, Angular Velocity] problem without given masses.

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SUMMARY

The problem involves calculating the maximum angular velocity of a meter stick suspended at a pivot point 0.26 meters from the top end, which is rotated to a horizontal position and released. The key concepts include Rotational Inertia, represented by the formula I = Σ m_i r_i², and the application of energy conservation principles. The discussion emphasizes the relationship between rotational kinetic energy and potential energy to determine the maximum angular velocity without needing the mass of the meter stick.

PREREQUISITES
  • Understanding of Rotational Inertia and its calculation.
  • Knowledge of torque and its role in rotational motion.
  • Familiarity with energy conservation principles in physics.
  • Basic concepts of angular velocity and rotational kinetic energy.
NEXT STEPS
  • Study the derivation and application of the Rotational Inertia formula.
  • Learn about torque and its calculation in rotational systems.
  • Explore energy conservation in rotational dynamics.
  • Investigate the relationship between potential energy and kinetic energy in rotational motion.
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Students and educators in physics, particularly those focusing on mechanics, as well as anyone interested in understanding the principles of rotational motion and energy conservation.

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Hello:

I seem to be stuck on this one problem: "A meter stick is suspended vertically at a pivot point 0.26 meters from the top end. It is rotated on the pivot until it is horizontal and then released from rest. What will be its maximum angular velocity (in radians per second)?"

So I figured this problem might involve Rotational Inertia: [tex]I=\sum_i m_{i} r_{i}^2[/tex]

Would I also need to find torque? (I'm getting confused on how the problem does not give me the mass of the meter stick.) Am I using the right formula?

Any help would be appreciated.
 
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You need to use energy conservation. If the angular velocity is maximal, what does that tell you about rotational kinetic energy? Further on, what does that tell you about potential energy?
 
Aha! You were dead on right about the energy conservation. Thanks for your help. :-)
 

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