If a merry-go-round makes 24 revs in 3 min?

Question

what is its average angular speed in rad/s?
if two people were on it one at 4.0 m and one at 5.0 m from the center, what would there their tangential speeds?

Answer 1

1 rev = 2*pi radians so

angular speed w =#radians/time = 2*pi*24/(3*60) = pi/90 = 0.035 rad/s

tangential speed v = w*r

v(4m) = 0.035*4 = 0.14 m/s

v(5m) = 0.17 m/s

Answer 2

one revolution corresponds to 2pi radians so 24 rev correspond to 48pi radians which is done in 3 min . 3 min is 180sec --so its angulare speed is 48pi divided by 180 which is (4pi / 15) radians per sec . the tangential speeds are (4
times 4pi / 15) m/s and (5 times 4pi over 15 m/sec). which come to 16pi/15 m / s and 4/3pi m per sec