Really could use some physics help.?

Question

A 45.0kg child stands near the edge of a merry-go-round in a local park. If the radius of the merry-go-round is 2.50 meters, and the coefficient of static friction between the child's shoes and the surface is 0.6, find the maximum angular speed of the merry-go-round if the child is not to fall off. (Assume the only centripetal force acting on the child is the friction between his shoes and the surface.

Answer 1

the centripetal acceleration is -w^2*r

that requires that
m*w^2*r=m*g*µs
at the maximum

solving for w
w=sqrt(g*µs/r)
plugging in the numbers
w=sqrt(9.81*0.6/2.5)
w=1.53 rad/sec

j