Non-uniform Circular Motion

In uniform circular motion, an object moves at constant speed along a circular path. Non-uniform circular motion occurs when an object travels in a circle while speeding up or slowing down. This introduces tangential acceleration in addition to radial acceleration, making the total acceleration vary with speed.

Tangential acceleration occurs when the speed of an object changes as it moves in a circle. It represents the rate of change of speed and acts tangent to the circular path. When the object speeds up, tangential acceleration aligns with the velocity vector; when slowing down, it opposes the velocity direction.

Radial acceleration, also called centripetal acceleration, depends on the object's speed. As speed increases, radial acceleration increases proportionally; as speed decreases, radial acceleration decreases. The magnitude of radial acceleration varies continuously throughout the motion, unlike in uniform circular motion where it remains constant.

Tangential acceleration equals zero at points of maximum and minimum speed. At these instants, the object is neither speeding up nor slowing down, so the rate of change of speed is zero. At all other points in the motion, tangential acceleration is nonzero.

Total acceleration is the vector sum of radial and tangential accelerations. The radial component points toward the center of the circle, while the tangential component acts along the velocity direction. The magnitude and direction of total acceleration vary with speed, being equal to radial acceleration only at maximum and minimum speeds.

A spinning top that slows down after being spun exhibits non-uniform circular motion, as does any accelerating rotor. Points on these objects move in circular paths while their speeds change, creating both radial and tangential accelerations. These examples show how tangential acceleration affects objects undergoing circular motion.

In non-uniform circular motion, velocity vector arrows of varying sizes show changes in speed. Larger arrows indicate faster speeds, while smaller arrows indicate slower speeds. The changing arrow sizes visually represent how the magnitude of velocity changes as the object moves along the circular path.