A merry-go-round accelerates from est at .870 rad/sec^2. When the merry-go-round has made 4 complete revolutions, how much time has elapsed since the merry-go round started?

Question

What is the angular velocity of the merry-go round?

Could someone help, please

Answer 1

a = angular acceleration
w = a t = angular velocity
theta = (1/2) a t^2 = radians turned total from rest
in this case thetas = 2pi * 4 = 8 pi radians
so
(1/2) a t^2 = 8 pi
you know a, get t and then w

Answer 2

to double check , the correct answer for time is 7.60 sec? and w is 6.61 rad/s?

Answer 3

(.87/2)t^2 = 8 pi
t = 7.599 yes 7.6
w = .87*7.6 = 6.61 yes