Non-uniform vertical circular motion

A roller coaster in a vertical circle will have a velocity change. This change in velocity will change the radial acceleration. My text book states that

“the car is changing only direction, not speed, at the very top and very bottom locations so at these points the acceleration is purely centripetal so Newton’s Second Law applies”.

Why this is only relevant at the top and bottom of the circle?

• Odd that the quote implies Newton's Second Law only applies at those two points. – M. Enns Jan 8 '17 at 4:50

In the top of the path, there is no component of the weight along the direction of motion. As a result, the entire weight is providing the required centripetal force for circular motion and there is no tangential acceleration. Hence, the acceleration is purely centripetal. But at other points on the path,there exist 2 components of the weight, one along the direction of the motion and another perpendicular to it. Due to this, the component of the weight along the direction of motion will increase its velocity, and the component perpendicular to it will change its direction 