In uniform circular motion, the velocity of an object moving in a circular path remains constant in magnitude but changes in direction continuously. If you decrease the radius of the circular path while keeping the speed (magnitude of velocity) constant, the velocity will increase.
This phenomenon can be explained using the concept of conservation of angular momentum. In uniform circular motion, the angular momentum of an object is conserved, which means it remains constant as long as no external torques act on the object. The angular momentum is given by the product of the moment of inertia (which depends on the mass distribution) and the angular velocity (which is related to the velocity in circular motion).
When the radius is decreased, the moment of inertia decreases because the mass is now distributed closer to the axis of rotation. Since the angular momentum remains constant, if the moment of inertia decreases, the angular velocity must increase to compensate and keep the product constant.
The angular velocity is directly related to the linear velocity in circular motion by the equation:
ω = v/r
Where ω is the angular velocity, v is the linear velocity, and r is the radius. If the radius decreases (r gets smaller), and the angular velocity remains constant (as it should in uniform circular motion), the linear velocity (v) must increase. Therefore, decreasing the radius in uniform circular motion leads to an increase in velocity.
To summarize, if you decrease the radius in uniform circular motion while keeping the speed constant, the velocity (magnitude of the velocity) of the object will increase.