Question

A manufacturer of CD-ROM drives claims that the player can spin the disc as frequently as 1200 revolutions per minute.

Answer 1

a. 7.0 m/s

First of all, we need to convert the angular speed (1200 rpm) from rpm to rad/s:

$\omega = 1200 \frac{rev}{min} \cdot \frac{2\pi rad/rev}{60 s/min}=125.6 rad/s$

Now we know that the row is located 5.6 cm from the centre of the disc:

r = 5.6 cm = 0.056 m

So we can find the tangential speed of the row as the product between the angular speed and the distance of the row from the centre of the circle:

$v=\omega r = (125.6 rad/s)(0.056 m)=7.0 m/s$

b.  $875 m/s^2$

The acceleration of the row of data (centripetal acceleration) is given by

$a=\frac{v^2}{r}$

where we have

v = 7.0 m/s is the tangential speed

r = 0.056 m is the distance of the row from the centre of the trajectory

Substituting numbers into the formula, we find

$a=\frac{(7.0 m/s)^2}{0.056 m}=875 m/s^2$