According to the law of conservation of angular momentum, when an object's radius decreases, its angular velocity must increase in order to maintain the same angular momentum. This is because the object's moment of inertia decreases as its radius decreases, requiring a higher angular velocity to maintain the same angular momentum.
The increase in velocity when radius decreases also affects the centripetal force acting on the object. The centripetal force is directly proportional to the square of the velocity, so as the velocity increases, the centripetal force must also increase to keep the object in its circular path.
One example is a figure skater performing a spin. When the skater pulls in their arms, their radius decreases and their angular velocity increases, causing them to spin faster. This is also why ice skaters extend their arms when they want to slow down or stop spinning.
No, this principle applies to any type of rotational motion, not just circular. For example, if a spinning top's radius decreases, its angular velocity will increase in order to maintain the same angular momentum.
As mentioned before, the law of conservation of angular momentum is at play here. This is a result of the conservation of energy, as a change in an object's kinetic energy (caused by the change in velocity) will result in an equal and opposite change in its potential energy. In this case, the change in kinetic energy is due to the change in velocity caused by the change in radius.