Question

The out side diameter of the playing area of an optical Blu-ray disc is 10.5cm, and the inside diameter is 4.75cm. When viewing movies, the disc rotates so that a laser maintains a constant linear speed relative to the disc of 8m/s as it tracks over the playing area.1) what is the maximum angular speed (rad/s) of the disc? 2) what is the minimum angular speed (rad/s) of the disc?

Answer 1

We will have the following:

1) The maximum angular speed of the disk is:

`v=r\omega\Rightarrow8=4.75\omega\Rightarrow\omega=(32)/(19)`
`\Rightarrow\omega\approx1.68`

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:

`8=10.5\omega\Rightarrow\omega=(16)/(21)`
`\Rightarrow\omega\approx0.76`

So, the minimum angular speed of the disk is 16/21 rad/sec or approximately 0.76 rad/sec.