The blades of an aeroplane propeller are rotating at the rate of 600 revolutions per minute. Its angular velocity is:

Options

A. (a)10 π rad/s
B. (b)20 π rad/s
C. (c)2 π rad/s
D. (d)7 π rad/s

Answer

To find the angular velocity of the blades of an aeroplane propeller rotating at a rate of 600 revolutions per minute (rpm), we can follow these steps:

### Step-by-Step Solution:

1. **Convert Revolutions per Minute to Revolutions per Second:**
- We know that 1 minute = 60 seconds.
- Therefore, to convert 600 revolutions per minute to revolutions per second, we divide by 60:
\[ \text{Frequency (f)} = \frac{600 \text{ revolutions}}{60 \text{ seconds}} = 10 \text{ revolutions per second} \]

2. **Use the Formula for Angular Velocity:**
- The angular velocity (\(\omega\)) in radians per second can be calculated using the formula:
\[ \omega = 2\pi f \]
- Here, \(f\) is the frequency in revolutions per second.

3. **Substitute the Frequency into the Angular Velocity Formula:**
- Now, substituting \(f = 10 \text{ revolutions per second}\) into the formula:
\[ \omega = 2\pi \times 10 = 20\pi \text{ radians per second} \]

4. **Final Answer:**
- Thus, the angular velocity of the aeroplane propeller is:
\[ \omega = 20\pi \text{ radians per second} \]