An amusement-park ride consists of a circular horizontal platform of radius 5.0 m that spins about a central vertical axis. For safety reasons, the magnitude of the linear speed of any rider at the rim must not exceed 8.0 m/s.
a. Part 1: Determine the maximum allowable angular speed of the platform in rad/s that satisfies the safety requirement.
b. Part 2: Calculate the corresponding rotation period of the platform in seconds.
c. Part 3: When the platform is rotating at this maximum allowable angular speed, a child is standing 3.0 m from the center. Find the magnitude of the child’s linear speed.