Kinematics of Inverted Physical Pendulum

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Homework Help Overview

The discussion revolves around the kinematics of an inverted physical pendulum, specifically analyzing the angular velocity of a stick as it falls to the table. The original poster presents the problem with equations related to angular acceleration and velocity, expressing uncertainty about the solution involving elliptic integrals.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the conservation of mechanical energy as a potential approach, questioning its applicability. There is discussion about the use of the parallel axis theorem and the distinction between rotational and translational kinetic energy.

Discussion Status

The conversation is ongoing, with participants examining different aspects of the problem. Some guidance has been offered regarding energy conservation and the application of the parallel axis theorem, but no consensus has been reached on the best approach to take.

Contextual Notes

There is mention of uncertainty regarding the use of elliptic integrals and numeric methods, as well as confusion about the role of translational kinetic energy in this context.

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Homework Statement



A stick of mass M, length L, stands upright on a table, pivoted to the table.

What is the angular velocity as it hits the table?


Homework Equations



ang. accel = (3g/2L)cos theta

w = (3g/2L) integral cos theta dt


The Attempt at a Solution



theta (t) = ?

Solution involves elliptic integrals?? Not familiar with numeric methods.

Any approximation of the velocity at the table would be good for now.
 
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Why don't you conserve mechanical energy?
 
aim1732 said:
Why don't you conserve mechanical energy?

Yeah this seems right. All you need to use is the parallel axis theorem, find the initial potential energy and solve for omega noting that the stick gains both rotational and translational kinetic energy.
 
Translational?
 
linear kinetic energy 1/2mv2 instead of 1/2Iw2

Actually thinking about it, it's not rolling so there probably wouldn't be translational kinetic energy gained.
 

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