Question

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?

Answer 1

Answer:

Child A.

Explanation:

• 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:

       $v_{t} = \omega * r (1)$

• 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.