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Calculate the centripetal force on the end of a 100 m (radius) wind turbine blade that is rotating at 0.5 rev/s. Assume the mass is 4 kg.
$4\times 10^{3}\textrm{ N}$
Solution Video

# OpenStax College Physics for AP® Courses Solution, Chapter 6, Problem 24 (Problems & Exercises) (1:26) #### Sign up to view this solution video!

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This is College Physics Answers with Shaun Dychko. A wind turbine blade has a length of 100 meters and so that's the distance from the tip of the blade to the axis of rotation at the center of the windmill. So if this is the blade here and here's the axis of rotation... it's this distance here that is 100 meters, that's r. The angular speed of rotation is 0.5 revolutions per second and we take this time of writing down the things we know as a chance to convert units into mks units that we will need in our formulas— meters, kilograms and seconds. So revolutions per second is not an mks unit, we want it to be in radians per second so we multiply by 2π radians per revolution and this gives 3.14159 radians per second. The mass of the turbine blade is 4 kilograms we are told. Okay... that's the little chunk of the end of it I guess. So centripetal force is that mass times the centripetal acceleration and we can substitute radius times angular speed squared in place of acceleration. So that's 4.0 kilograms times 100 meters times 3.14159 radians per second squared giving a force with one significant figure since that's the number of significant figures in the mass of 4 times 10 to the 3 newtons.