Final answer:
The new angular speed when the man walks closer to the center is 0.267 rev/s or 1.6 rpm. The change in kinetic energy is 58 J. This change in kinetic energy is due to the work done by the man as he moves toward the center of the merry-go-round.
Step-by-step explanation:
To determine the new angular velocity when the man walks to a point 1.0 m from the center, we can use the conservation of angular momentum. The initial angular momentum of the system is equal to the final angular momentum of the system.
The initial angular momentum is given by: Li = Im × ωi where Im is the moment of inertia of the merry-go-round and ωi is the initial angular velocity.
The final angular momentum is given by: Lf = Im × ωf + Ip × ωp where Ip is the moment of inertia of the man and ωp is the final angular velocity of the man.
Since the merry-go-round is a solid cylinder, the moment of inertia of the man can be calculated using the formula: Ip = m×r2 where m is the mass of the man and r is the distance from the axis of rotation.
Substituting the given values into the equations and solving for ωf, we find that the new angular speed is 0.267 rev/s or 1.6 rpm.
The change in kinetic energy can be calculated using the formula: ΔK = Kf - Ki where Kf is the final kinetic energy and Ki is the initial kinetic energy.
The initial kinetic energy is given by: Ki = 0.5 ωi2 Im + 0.5 ωi2 Ip.
The final kinetic energy is given by: Kf = 0.5 ωf2 Im + 0.5 ωf2 Ip.
Substituting the given values into the equations and solving for ΔK, we find that the change in kinetic energy is 58 J.
The change in kinetic energy is due to the work done by the man as he walks toward the center of the merry-go-round. When the man moves closer to the center, his rotational inertia decreases, resulting in a change in angular velocity. This change in angular velocity leads to a change in kinetic energy.