Final answer:
In a rotating disk, the centripetal force keeps mass elements moving in a circular path, and angular momentum remains constant if no external torques are applied. The centrifugal force acts outward in a rotating frame but does not exist in an inertial frame. Angular velocity remains constant if no energy is lost or external torques are applied.
Step-by-step explanation:
The question pertains to the dynamics of a rotating disk, more specifically, the changes in forces and motion as it rotates. When a disk of radius r rotates about its center with constant angular velocity, the centripetal force acting on any mass element of the disk remains directed towards the center. This force is necessary to keep the mass element moving along a circular path and is directly proportional to the mass and the square of the velocity of the rotating body, and inversely proportional to the radius (r) of the rotation.
Angular momentum of a rotating rigid body is the product of its moment of inertia and its angular velocity. If no external torques act on the disk, the angular momentum remains constant due to the principle of conservation of angular momentum. However, if we assume the mass remains constant, and there is an external torque, angular momentum could potentially increase or decrease depending on the direction of the torque.
Centrifugal force is an apparent force that acts outward on a mass when it is rotated. This force is felt by observers in the rotating reference frame and is proportional to the mass and the square of the velocity, and it increases with distance from the axis of rotation. In an inertial frame of reference (i.e., from an observer outside the rotating system), centrifugal force does not exist; rather, what is perceived as centrifugal force is the inertia of the mass attempting to travel in a straight line.
If the net external torque is zero and no energy is added or lost, the angular velocity of the disk will remain constant due to the conservation of angular momentum. However, it's important to note that if the radius were to change, in order to conserve angular momentum, the angular velocity would have to adjust inversely to the change in moment of inertia.