Solution: Because the circle P is tangent to the X axis at points O and P (0, 1), the radius of the circle P is 1.

When the circle P rolls along the positive direction of the X axis and the point A falls on the X axis for the first time, the length of OA is the same as that of the arc OA, so the abscissa of the point A is positive, which is equal to the length of the arc OA.

Because the angle apo = 120 degrees, the length of the lower arc AO is (120/360)2 pie r=2/3 pie.

So the abscissa of a is: 2/3 pie.

PS: I can't find the input of pi in mathematics, so I have to use Chinese characters instead.