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?
OpenStax College Physics for AP® Courses, Chapter 6, Problem 2 (Problems & Exercises)
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 2π radians for every revolution. So 1 complete circle has 2π radians so this is our conversion factor 2π radians per revolution. The revolution units cancel leaving us with radians. So we have 6 divided by 60 multiplied by 2π which is 0.6 radians per second.