Minimal angular velocity of a swinging homogenous stick ?

AI Thread Summary
To determine the minimal angular velocity for a homogeneous stick to complete a full rotation around its end axis, the discussion emphasizes the need to analyze the potential and kinetic energy at the balance point. The swing time for small displacements is provided, allowing the use of the Maclaurin series to approximate sin(θ). The approach involves calculating potential energy at the highest point and kinetic energy at the lowest point, although the mass of the stick is not specified. It is suggested that the mass may not be necessary for solving the problem if the swing time is known. The focus remains on understanding energy conservation principles in the context of the stick's motion.
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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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