Explanation:

Moment of Inertia:
The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution of the object and the axis of rotation. By spreading his arms or curling up, the man changes the distribution of his mass and hence changes his moment of inertia. When he spreads his arms, his moment of inertia increases as the mass is distributed farther from the axis of rotation. When he curls up, his moment of inertia decreases as the mass is brought closer to the axis of rotation.

Angular Velocity:
Angular velocity is the rate at which an object rotates around an axis. It is defined as the change in angular displacement per unit time. When the man changes the shape of his body, he can change his angular velocity. By spreading his arms, he increases his moment of inertia, which results in a decrease in his angular velocity. This is because angular momentum is conserved, and as moment of inertia increases, angular velocity decreases. When he curls up, he decreases his moment of inertia, which results in an increase in his angular velocity.

Rotational Kinetic Energy:
Rotational kinetic energy is the energy associated with an object's rotational motion. It depends on the moment of inertia and the angular velocity of the object. By changing the shape of his body, the man can also change his rotational kinetic energy. When he spreads his arms, his moment of inertia increases and his angular velocity decreases. As a result, his rotational kinetic energy decreases. When he curls up, his moment of inertia decreases and his angular velocity increases. As a result, his rotational kinetic energy increases.

In conclusion, by changing the shape of his body, the man can change his moment of inertia, angular velocity, and rotational kinetic energy. Spreading his arms increases moment of inertia, decreases angular velocity, and decreases rotational kinetic energy. Curling up decreases moment of inertia, increases angular velocity, and increases rotational kinetic energy.