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As in many applied mathematics problems, the first part of the problem involves making the right equation from the given facts. Such aspects are important and often a major part of the the problem solving process.


Finding $V_{crit}$

The total rotational force (moment) on each of the arms is $M = \int^L_0{F}dx$. Moment and torque are equivalent.

Rotational version of Power = Force $\times$ Velocity

For the two terms on the right hand side, use their rotational equivalents.