Problem: An object goes around a circle every 1.7 seconds. How many revolutions would this be in a second? How many radians in a second? How fast would the object be moving on a circle of radius 2 meters?
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Solution: In 1.7 seconds this is one revolution, so in 1 second there would be 1/ 1.7 = .5882 revolutions (imagine counting to 1 by 1.7s).
Since a revolution corresponds to 2 `pi radians, .5882 revolutions per second is 2 `pi ( .5882) radians per second = 3.695 radians per second.
On a circle of radius 2 meters, 1 radian would correspond to a distance of 2 meters, so 3.695 radians per second would be 2( 3.695) meters per second = 7.39 meters per second.