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Microwave ovens rotate at a rate of about 6 rev/min. What is this in revolutions per second? What is the angular velocity in radians per second?
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Final Answer
$0.1 \textrm{ rev/s}$
$0.6 \textrm{ rad/s}$
Solution Video

OpenStax College Physics Solution, Chapter 6, Problem 2 (Problems & Exercises) (0:58)

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Video Transcript

This is College Physics Answers with Shaun Dychko. A microwave turntable spins at 6 revolutions per minute and we have to express that in revolutions per second so we multiply by a conversion factor of 1 minute for every 60 seconds and the minute units cancel because they are on opposite sides of this fraction leaving us with revolutions per second, I should say so that's 0.1 revolutions per second. A different way to express that angular speed is to say 6 revolutions per minute times 1 minute per 60 seconds— again getting rid of the minutes and replacing the units in the denominator with seconds— we can then multiply that by 2<i>π</i> radians for every revolution. So 1 complete circle has 2<i>π</i> radians so this is our conversion factor 2<i>π</i> radians per revolution. The revolution units cancel leaving us with radians. So we have 6 divided by 60 multiplied by 2<i>π</i> which is 0.6 radians per second.