8. As shown in Figure 2, a circle $\odot O$ with radius $r$ rolls without slipping along the broken line $A B C D E$. If $A B=B C=C D=D E=2 \pi r, \angle A B C=\angle C D E=150^{\circ}$, $\angle B C D=120^{\circ}$, then $\odot O$ rotates through _____ turns from point $A$ to point $E$.
8. $4 \frac{1}{3}$.

From $A B=B C=C D=D E=2 \pi r$, we get that when $\odot O$ rolls along the line segments $A B, B C, C D, D E$, it rotates 1 week each;

From $\angle A B C=\angle C D E=150^{\circ}$, we get that when $\odot O$ passes through points $B$ and $D$, it rotates an additional $\frac{1}{12}$ week each;

From $\angle B C D=120^{\circ}$, we get that when $\odot O$ passes through point $C$, it rotates an additional $\frac{1}{6}$ week.
Therefore, $\odot O$ rotates $4+\frac{1}{12}+\frac{1}{6}+\frac{1}{12}=4 \frac{1}{3}$ (weeks) from point $A$ to $E$.