Question

A DVD rotates through an angle of 20π radians in a second. At this speed how many revolutions does the DVD make in 30 seconds?

Answer 1

(20pi radians/1 second)*(30 seconds) = (20pi*30) radians

(20pi radians/1 second)*(30 seconds) = 600pi radians


So in 30 seconds, it rotates 600pi radians


2pi radians = 1 rev


which allows us to say

(600pi radians)*(1 rev/2pi radians) = (600pi/2pi) rev

(600pi radians)*(1 rev/2pi radians) = 300 rev


So in 30 seconds, it completes 300 full revolutions