We will have the following:
1) The maximum angular speed of the disk is:
[tex]v=r\omega\Rightarrow8=4.75\omega\Rightarrow\omega=\frac{32}{19}[/tex][tex]\Rightarrow\omega\approx1.68[/tex]So, the maximum angular speed of the disk is 32/19 rad/sec or approximately 1.68 rad/sec.
2) The minimum angular speed of the disk is:
[tex]8=10.5\omega\Rightarrow\omega=\frac{16}{21}[/tex][tex]\Rightarrow\omega\approx0.76[/tex]So, the minimum angular speed of the disk is 16/21 rad/sec or approximately 0.76 rad/sec.