What is non-uniform circular motion?
If the speed of the object in circular motion is not constant, then we have non-uniform circular motion. For example, when the bob attached to a string moves in a vertical circle, the speed of the bob is not the same at all times Whenever the speed is not the same in a circular motion, the particle will have both centripetal and tangential acceleration.
Concept: Concept of Rest and Motion
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Chapter 2: Kinematics - Evaluation [Page 100]