Question

In a circular motion,why does the acceleration
tangential to the circle equal (2r'w + rw')?(r:radius;w:angular velocity)

Answer 1

This is not correct, in a circular motion, the radius is fixed: r = R, so r' = 0.
Tangential acceleration is simply: \(\dot v=R \dot\omega = R\alpha\)

The expression you wrote is the general expression in cylindrical coordinates.