a CD has a diameter of 110 millimeters. When playing audio, the angular speed varies to keep the linear speed constant where the disc is being read. When reading along the outer edge of the disc, the angular speed is about 220 RPM (revolutions per minute). Find the linear speed. 

To find the linear speed when reading the outer edge of the CD, we can use the relationship between angular speed and linear speed. The formula for this is:

\[
v = r \cdot \omega
\]

Where:
- \( v \) is the linear speed.
- \( r \) is the radius of the CD.
- \( \omega \) is the angular speed (in radians per second).

### Step 1: Convert the diameter to radius.
Since the diameter of the CD is 110 mm, the radius is half of that:

\[
r = \frac{110 \text{ mm}}{2} = 55 \text{ mm} = 0.055 \text{ meters}
\]

### Step 2: Convert the angular speed from RPM to radians per second.
We are given the angular speed as 220 RPM (revolutions per minute). To convert RPM to radians per second:

\[
\omega = 220 \text{ RPM} \times \frac{2\pi \text{ radians}}{1 \text{ revolution}} \times \frac{1 \text{ minute}}{60 \text{ seconds}}
\]

\[
\omega = 220 \times \frac{2\pi}{60}
\]

Let’s calculate this.

\[
\omega = \frac{440\pi}{60} \approx 23.04 \text{ radians/second}
\]

### Step 3: Calculate the linear speed.
Now, we can plug in the values into the linear speed formula:

\[
v = r \cdot \omega = 0.055 \text{ m} \cdot 23.04 \text{ rad/s}
\]

\[
v \approx 1.267 \text{ meters per second}
\]

Thus, the linear speed is approximately **1.27 meters per second**.

Would you like further details or have any questions?

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Here are five related questions to expand on the topic:
1. How does the angular speed change when reading closer to the center of the CD?
2. What would the linear speed be at the innermost part of the disc if the radius is much smaller?
3. Why does the CD player keep the linear speed constant during playback?
4. How do you convert linear speed back to angular speed if the radius and speed are known?
5. How does the concept of angular velocity apply to other rotating objects like hard drives?

**Tip:** Always ensure units are consistent when using physical equations—convert millimeters to meters, RPM to radians per second, etc.

A CD has a diameter of 110 millimeters. When playing audio, the angular speed varies to keep the linear speed constant where the disc is being read. When reading along the outer edge of the disc, the angular speed is about 220 RPM (revolutions per minute). Find the linear speed.

Learn how to calculate the linear speed of a CD when its angular speed is 220 RPM along the outer edge. Using concepts from circular motion, this problem demonstrates the relationship between angular velocity and linear velocity with detailed step-by-step solutions. Suitable for Grades 10-12.

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