Question
Suppose a piece of dust finds itself on a CD. If the spin rate of the CD is 500 rpm, and the piece of dust is 4.3 cm from the center, what is the total distance traveled by the dust in 3 minutes? (Ignore accelerations due to getting the CD rotating.)
Final Answer
Solution video
OpenStax College Physics for AP® Courses, Chapter 10, Problem 6 (Problems & Exercises)
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This is College Physics Answers with Shaun Dychko. A piece of dust is on a CD which is spinning at 500 rpm; we'll use this chance when we write down our known's to also do our unit conversions so we don't have to worry about those later. So we have 500 rpm times 2π radians per revolution so that means the revolution's cancel that's the 'r' part of rpm— revolutions per minute— and then we multiply it by 1 minute for every 60 seconds and this rpm can be written as 'r' per 'm' and so this 'm' is really on the bottom— standing for minutes— and this cancels with these minutes and we are left with radians per second. So this is 52.3599 radians per second. The piece of dust is positioned 4.3 centimeters from the axis of rotation of the CD; we multiply that by 1 meter for every 100 centimeters giving 0.043 meters and the time that it's spinning is 3 minutes which is 180 seconds. So the distance that the piece of dust travels is its tangental or linear velocity multiplied by time and its tangental velocity is given by the angular velocity multiplied by its distance from the axis of rotation. So we substitute ωr in place of v in this formula for d and then we plug in all of our numbers. So that's 52.3599 radians per second times 0.043 meters from the center times 180 seconds which is 405 meters traveled during this 3 minutes.