Question

A merry-go-round has an angular velocity of 5.20 rad/s. A ribbon is tied at the end of one of the arms and it has speed of 3.60 m/s. At what distance is the ribbon from the center of the merry-go-round?

Answer 1

as with arc length and angle, s=rθ,
ds/dt = r dθ/dt

v = rω

so, plug in your numbers