6. (10 points) As shown in the figure, there are three adjacent large, medium, and small circles with radii of $9 \mathrm{~cm}, 3 \mathrm{~cm}, 1 \mathrm{~cm}$ respectively; the medium circle rolls clockwise downward along the inside of the large circle; the small circle rolls counterclockwise upward along the inside of the medium circle, both at a speed of 1 centimeter per second along the circumference. If a fixed arrow is attached to the small circle, then during the process of the medium circle rolling one full circle and returning to the starting point, the rotation angle of the arrow (the small circle rotating around its own center) is. degrees.
2520
【Solution】Solution:
The ratio of the radii of the large circle to the medium circle is $3: 1$, which means the circumference of the large circle is 3 times that of the medium circle. If the medium circle rolls along the circumference of the large circle in a clockwise straight line, it will rotate 3 times around its own center; now, the medium circle rotates counterclockwise once inside the large circle, so the medium circle has actually rotated 2 times clockwise around its own center; similarly, the small circle rotates counterclockwise once inside the medium circle, which means it actually rotates 2 times counterclockwise around its own center, so when the small circle revolves around the medium circle 3 times, it actually rotates 6 times around its own center. Since the small circle rotates while the medium circle rotates counterclockwise once around the large circle, the small circle actually rotates 7 times counterclockwise in total.
$$
360 \times 7=2520
$$

Therefore, the answer is: 2520