Two children are riding on a rotating merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger tangential speed?
For all points on the merry-go-round, the angular speed ω is the same, as it's the rate of change of the angle rotated regarding time, and all points along the same radius rotate at the same time.
Based on the definition of angular velocity, and the definition of angle, we find that there exists a fixed relationship between the angular speed and the tangential speed, as follows:
[tex]v_{t} = \omega * r (1)[/tex]
So, since ω remains constant, the tangential speed is directly proportional to the distance from the axis of rotation r.
This means that it will be larger for the child A, who is at a greater distance from the axis of rotation than child B.
