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Question
A helicopter blade spins at exactly 100 revolutions per minute. Its tip is 5.00 m from the center of rotation. (a) Calculate the average speed of the blade tip in the helicopter's frame of reference. (b) What is its average velocity over one revolution?
Question by OpenStax is licensed under CC BY 4.0.
Final Answer
  1. $52\textrm{ m/s}$
  2. The blade tip has zero displacement since it returns to its starting position after one revolution. It therefore has zero average velocity.
Solution Video

OpenStax College Physics Solution, Chapter 2, Problem 6 (Problems & Exercises) (1:41)

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Video Transcript

This is College Physics Answers with Shaun Dychko. This helicopter blade has a radius of 5 meters, that's the distance from the tip to the center of the rotor, and it has an angular speed of 100 revolutions per minute and this <i>ω</i> is the traditional symbol for angular speed. Now we want to find out what is the average speed of this tip as it travels in this circle and so the distance that it travels will be the circumference of this circle and we need to know how much times it takes to do that one revolution. So we have our expression for speed here is distance over time and the distance we are substituting with the circumference of a circle formula, 2<i>π</i> times <i>r</i>, and we are dividing by time and we need to figure out what is the time based on this angular speed that we are given. So we are told that it takes 1 minute for 100 revolutions and I have substituted in 60 seconds for every 100 revolutions and this works out to 0.60 seconds for one turn. So we substitute in 0.60 seconds in here because the distance is the distance of one turn and then we are dividing by the time for one turn. And so we have the speed then is 2<i>π</i> times the radius of 5 meters divided by 0.60 seconds giving us 52 meters per second. And part (b) asks us for the average velocity after one revolution. and the blade tip has no displacement though after a revolution because it returns back to its starting point so the average velocity is zero.