The information on a compact disk is scanned by a laser initially at a radius of 2.4 cm and then out to a maximum of 6.0 cm. Because the dimensions of the pit information remain constant with radius, the disk motor adjusts so that the tangential velocity remains constant. What is the ratio of the inner to outer rotational frequencies?
A) 0.16
B) 6.3
C) 1.0
D) 2.5
E) 0.40

Question

Quizplus · Accepted Answer

Since the tangential velocity must be constant, the angular velocity must increase as the radius increases. From the formula for tangential velocity, $v=\omega r$, we have $v=	ext{constant} \Rightarrow \omega \propto r^{-1}$. Therefore, the ratio of the inner to outer rotational frequencies is $\frac{\omega_{	ext{inner}}}{\omega_{	ext{outer}}}=\frac{r_{	ext{outer}}}{r_{	ext{inner}}}=\frac{6.0	ext{ cm}}{2.4	ext{ cm}}=\boxed{2.5	ext{ (D)}}$.

The Information on a Compact Disk Is Scanned by a Laser