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'Turbo Turbines' printed from https://nrich.maths.org/
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.