A manufacturer of CD drives claims that the player can spin the disc as frequencly as 1200 revolutioins per minute. If the spinning is at this rate, what is the speed (in m/s) of the outer row of data on the disc, this row is located 5.6 cm from the center of the disc?

Answer

To solve the problem of finding the speed of the outer row of data on a CD spinning at 1200 revolutions per minute (RPM) and located 5.6 cm from the center, we can follow these steps:

### Step 1: Convert the radius from centimeters to meters
The radius \( r \) is given as 5.6 cm. We need to convert this to meters for consistency in SI units.

\[ r = 5.6 \, \text{cm} = 5.6 \times 10^{-2} \, \text{m} \]

### Step 2: Convert the rotational speed from RPM to radians per second
The angular speed \( \omega \) in radians per second can be calculated from the RPM. We know that:

\[ \omega = \text{RPM} \times \frac{2\pi \, \text{radians}}{1 \, \text{revolution}} \times \frac{1 \, \text{minute}}{60 \, \text{seconds}} \]

Substituting the given value:

\[ \omega = 1200 \, \text{RPM} \times \frac{2\pi}{60} \]

Calculating this gives:

\[ \omega = 1200 \times \frac{2\pi}{60} = 40\pi \, \text{radians/second} \]

### Step 3: Use the relationship between linear speed and angular speed
The linear speed \( V \) at the outer row can be calculated using the formula:

\[ V = r \times \omega \]

Substituting the values we have:

\[ V = (5.6 \times 10^{-2} \, \text{m}) \times (40\pi \, \text{radians/second}) \]

### Step 4: Calculate the linear speed
Now we can calculate \( V \):

\[ V = 5.6 \times 10^{-2} \times 40\pi \approx 7.03 \, \text{m/s} \]

### Final Answer
The speed of the outer row of data on the CD is approximately \( 7.03 \, \text{m/s} \).

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