When the man drops the two masses without moving his arms, the conservation of angular momentum applies. According to the law of conservation of angular momentum, the total angular momentum of a system remains constant when no external torques act on it.
Initially, when the man is holding the masses at arms' length and rotating, he possesses a certain angular momentum. Let's assume this initial angular momentum as L_initial.
When the man drops the masses, they will start moving independently. As the masses move closer to the center of rotation (towards the man's body), their moment of inertia decreases. Since angular momentum is given by the product of moment of inertia and angular velocity (L = I * ω), a decrease in moment of inertia would result in an increase in angular velocity to maintain the conservation of angular momentum.
Therefore, as the masses move closer to the center, the man's moment of inertia decreases, and to conserve angular momentum, his angular velocity (ω) increases. This increase in angular velocity is known as the "ice skater effect" or "figure skater effect," where a spinning skater increases their rotational speed by pulling their arms closer to their body.
In summary, when the man drops the masses without moving his arms, his angular velocity increases due to the conservation of angular momentum.