When a man is sitting on a rotating stool with his arms outstretched, he is essentially increasing his moment of inertia. This means that the rotational inertia or angular momentum of the system is higher.

When the man suddenly folds his arms, his moment of inertia decreases. Moment of inertia is directly proportional to the angular velocity (rotational speed).

Therefore, when he folds his arms, the moment of inertia decreases and the angular velocity increases. This is because conservation of angular momentum states that the product of moment of inertia and angular velocity remains constant in the absence of any external torque.

Hence, the correct answer is option 1 - the angular velocity of the man would increase.

It is important to note that if there was no external torque acting on the system, the angular momentum would remain constant. However, in this case, the man folding his arms would cause a change in the moment of inertia, leading to a change in the angular velocity.