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And the effect of centripetal acceleration is to cause a rate of change of angular velocity.
Look bro, centripetal acceleration causes body to move in a circle, the angular velocity is ONLY a property of circular motion.
What I was trying to tell was An object can't move in a uniform circle with a constant angular velocity.
This is the whole problem. It's quiet the opposite! If the angular velocity actually changes and the force remains the same, then the radius would constantly decrease ( F = mw^2r ) which means that the motion will no longer be uniform!
Let's understand this by a simple example, if I tie a ball to the end of a rope and keep moving it in a circle. By your claim, it is impossible to move in a circular motion without the rope being cut. Why? Because radius and mass are constant and the omega "should" be changing thus the force should be increasing! It will increase to a certain point that the rope will not be able to provide the necessary tension. so it will be cut.
This is of course not true...
And no , when I wrote when the velocity is constant, there's no acceleration, I wasn't referring to rotational motion, but I was trying to refer to translatory motion, and later analyse both the motions in order to get to the right point.
Whichever motion you're referring to, you'll get the same answer. Let's think about something, if you have a ball moving in a circle with constant angular speed and velocity, and you gradually increase the magnitude of the velocity. What will happen to the angular speed? It will ALSO increase both practically and technically since v = wr. This means that if the speed is constant, then the angular velocity should be also constant, again both practically and technically.
However, to keep moving in a circular motion, a force is needed to cause a constant change in the direction of the velocity. This force causes centripetal acceleration which does NOT change the magnitude of the velocity rather its direction ( By definition ). If there is no change in magnitude, there is no change in angular velocity BUT there is a centripetal acceleration.
If either the velocity or the angular velocity somehow change ( they're actually connected so if one does change then the other will change as well ) .... Then the motion will be distorted and won't be a uniform circular motion... Unless the force varies as well and to some extinct the circular motion will be distorted as the radius would gradually change...
Hope that helped...