Question

Andrea and Chuck are riding on a merry-go-round. Andrea rides on a horse at the outer rim of the circular platform, twice as far from the center of the circular platform as Chuck, who rides on an inner horse. When the merry-go-round is rotating at a constant angular speed, Andrea's tangential speed is which of the following? a) twice Chuck's b) the same as Chuck's c) half of Chuck's d) impossible to determine B. When the merry go round is rotating at a constant angular speed, Andrea's tangential speed is a) twice Chuck's b) the same as Chuck's

Answer 1

Answer: a) Twice Chuck's

Step-by-step explanation:

If the angular speed is constant, as the merry - go -round is a rigid body, so the distance between two points must remain the same, it is needed that the points farther the center, move faster than the ones closer to it.

There exists a relationship between tangential and angular speed, as follows, that relates the definitions of linear and angular speed, and the angle definition:

angle = arc / radius ⇒ Δθ/Δt = Δs/Δt / r ⇒ ω = v/r ⇒ v = ω. r

If ω is constant, v is directly proportional to r, distance to the center (radius in a circular platform), so if r is twice for Andrea, her tangential speed must be twice Chuck's.