Final answer:
The rotational kinetic energy of the system can be calculated using the formula Rotational Kinetic Energy = (1/2) * moment of inertia * angular velocity^2. To find the moment of inertia, we need to consider the individual moments of inertia of the disc and the annular cylinder that make up the platform. The moment of inertia of a disc is given by the formula Moment of inertia = (1/2) * mass * radius^2.
Step-by-step explanation:
The rotational kinetic energy of a system can be calculated using the formula:
Rotational Kinetic Energy = (1/2) * moment of inertia * angular velocity^2
To find the moment of inertia of the system, we need to consider the individual moments of inertia of the disc and the annular cylinder that make up the platform. The moment of inertia of a disc is given by the formula: Moment of inertia = (1/2) * mass * radius^2. The moment of inertia of an annular cylinder is given by the formula: Moment of inertia = (1/2) * mass * (outer radius^2 + inner radius^2). Once we have the moment of inertia, we can substitute it into the rotational kinetic energy formula along with the given angular velocity to calculate the rotational kinetic energy of the system.
Using the given values:
Mass of the person (m) = 70 kg
Mass of the platform (M) = 750 kg
Radius of the platform (R) = 1.2 m
Angular velocity (ω) = 1 revolution / 5 seconds = 2π rad / 5 seconds
Calculating the moment of inertia of the system:
Moment of inertia of the disc (Idisc) = (1/2) * 70 kg * (0.6 m)^2 = 12.6 kg m2
Moment of inertia of the annular cylinder (Icylinder) = (1/2) * 750 kg * ((1.2 m)^2 + (0.6 m)^2) = 927 kg m2
Moment of inertia of the system (I) = Idisc + Icylinder = 12.6 kg m2 + 927 kg m2 = 939.6 kg m2
Calculating the rotational kinetic energy of the system:
Rotational Kinetic Energy = (1/2) * 939.6 kg m2 * (2π rad / 5 seconds)^2 = 710 J