Question

A rotating merry go-round makes one complete revolution in 4.2 s. (a) what is the linear speed of a child seated 1.3 m from the center?

Answer 1

Remember in solving any Physics problem it is important to write all the given parameter. Given are 1 complete revolution of merry go-round or can be written as 1rev/s, this should be converted to radians, since it makes one complete revolution. Radius given equal to 1.3 m from the center. Simply follow the process,  ω=1rev/s x 2πrads/rev  ω=answer will in "rad/s" or cancel the unit "rev". The formula to follow is Speed=rω. just multiply radius and the angular speed. 

Answer 2

The radius, r, of the child from the center of the wheel is
r = 1.3 m

The wheel makes one revolution in 4.2 s. Its angular velocity is
ω = (2π rad)/(4.2 s) = 1.496 rad/s

The linear speed of the child is the tangential velocity, given by
v = rω
= (1.3 m)*(1.496 rad/s)
= 1.945 m/s

Answer: 1.95 m/s (nearest hundredth)