Minimal angular velocity of a swinging homogenous stick ?

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SUMMARY

The discussion focuses on calculating the minimal angular velocity required for a homogeneous stick to complete a full rotation when swinging around its end axis. The problem involves using the swing time for small displacements and the Maclaurin series to approximate the behavior of the pendulum. Participants suggest analyzing potential and kinetic energy at the balance point, emphasizing that the mass of the stick is not necessary for solving the problem, as the energy equations can be utilized without it.

PREREQUISITES
  • Understanding of angular velocity and its implications in rotational motion.
  • Familiarity with potential and kinetic energy concepts in physics.
  • Knowledge of the Maclaurin series for approximating functions.
  • Basic principles of pendulum motion and period calculations.
NEXT STEPS
  • Explore the derivation of the period of a simple pendulum using the formula T = 2π√(L/g).
  • Investigate the application of the conservation of energy principle in rotational dynamics.
  • Learn about the implications of mass distribution in rigid body dynamics.
  • Study the effects of angular displacement on the motion of pendulums and similar systems.
USEFUL FOR

Physics students, educators, and anyone interested in understanding rotational dynamics and energy conservation principles in pendulum systems.

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Homework Statement



Find the required angular velocity of the stick swinging around it's end axis (like a simple pendulum only without the added mass) at the point of "balance" (where the sinus function crosses the x-axis I suppose, sorry for the "weird" translation) so that it will be able to make one full rotation.

I am given it's length and it's "swing time" for small displacements (getting sin(θ) = θ using the Maclaurin series)


Homework Equations





The Attempt at a Solution



I have attempted it by setting the potential energy at the above position at full and kinetic at zero, but I am not given a mass for the stick, and I doubt my approach was very sane given the problem.
 
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If you know the swing time, can you find the mass by using the formula for the period of a pendulum?
 
Assume the mass is given. Work out the kinetic and potential energies of the stick. Then see if you really need the mass to solve the problem.
 

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