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

Options

A. 10 `pi` rad/s
B. 20 `pi` rad/s
C. 2 `pi` rad/s
D. 7 `pi` 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. **Understand the relationship between revolutions and radians**:
- One complete revolution corresponds to an angle of \(2\pi\) radians.

2. **Convert revolutions per minute to radians per minute**:
- Since the propeller is rotating at 600 revolutions per minute, we can convert this to radians per minute:
\[ \text{Radians per minute} = 600 \text{ revolutions/min} \times 2\pi \text{ radians/revolution} = 1200\pi \text{ radians/min} \]

3. **Convert radians per minute to radians per second**:
- To convert the angular velocity from radians per minute to radians per second, we divide by 60 (since there are 60 seconds in a minute):
\[ \text{Radians per second} = \frac{1200\pi \text{ radians/min}}{60} = 20\pi \text{ radians/sec} \]

4. **Final answer**:
- The angular velocity (\(\omega\)) of the propeller blades is:
\[ \omega = 20\pi \text{ radians/sec} \]