Question

A merry-go-round at a playground is a circular platform that is mounted parallel to the ground and can rotate about an axis that is perpendicular to the platform at its center. the angular speed of the merry-go-round is constant, and a child at a distance of 1.4 m from the axis has a tangential speed of 2.2 m/s. what is the tangential speed of another child, who is located at a distance of 2.1 m from the axis?

Answer 1

Since angular speed is persistent, v/r is constant.
Where:

v is tangential speed; and

r is distance from axis.

Then equate v/r in both cases to get v in the second case.

Hence, speed = 2.2 x 2.1 / 1.4 meters

= 3.3 meters / seconds

Alternative solution would be:

w = 2.2 / 1.4 = 1.57

v = rw = 2.1 x 1.57 = 3.3 meters / seconds