A runner travels around a circular track of radius 70 meters.  Her speed is a constant 2m/s.  If she runs for 30 minutes,

find total meters moved
first get time in seconds==> 30min*60sec/1min=1800sec
distance=s*t ==> 2m/s*1800s = 3600m

give speed in radians/sec
for this circle, radius = 70m, so when runner goes 70m, she goes one radian, so...
2m/s*1radian/70m=.03rad/s

find total laps
one lap=one circumference=2pradius==>(2)(p)(70m)= 439.8m
total dist/one lap=total laps.... 3600m/(439.8m/lap)= 8.2 laps
OR
51.43radians moved/2pradians per lap=8.2 laps

find displacement from start point
distance from start is whatever decimal is left over after the 8th lap.... or .2 laps

find total radians moved
for this circle, r=70m, so when traveling along radius if you go 3600m, then you have gone 3600m/70m =51.43radians
notice that the meters cancel, leaving us with NO units!  We refer to this "natural" way of describing a circle as a radian

how many degrees did she go total?
51.43radians*57.3degrees/1radian=  2946.7°