A CD has a diameter of 12.0 cm. If the CD is rotating at a constant frequency of 6.00 cycles per second, then the angular velocity is what?

To find the angular velocity, we can use the formula:

\[
\omega = 2\pi f
\]

where:
- \(\omega\) is the angular velocity (in radians per second),
- \(f\) is the frequency (in cycles per second or Hertz),
- \(\pi\) is a mathematical constant approximately equal to 3.1416.

Given:
- \(f = 6.00 \, \text{cycles per second (Hz)}\),

We substitute the value of \(f\) into the formula:

\[
\omega = 2\pi \times 6.00
\]

\[
\omega = 12\pi \, \text{radians per second}
\]

\[
\omega \approx 37.70 \, \text{radians per second}
\]

So, the angular velocity is approximately **37.70 radians per second**.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. How is angular velocity related to linear velocity?
2. What is the period of rotation for the CD?
3. How does the radius of the CD affect the linear speed at the edge?
4. If the frequency doubled, what would be the new angular velocity?
5. What is the total angle in radians covered in 2 seconds?

**Tip:** Angular velocity is always expressed in radians per second, regardless of whether the object is rotating at a constant or varying rate.

Learn how to calculate the angular velocity of a CD with a diameter of 12.0 cm rotating at 6.00 cycles per second. This problem uses the formula ω = 2πf and is suitable for students in Grades 9-12, covering concepts like angular velocity, frequency, and radians.

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