A fly wheel is rotating about its own axis at an angular velocity `11 rads^(-1)`, its angular velocity in revolution per minute is

Options

A. 105
B. 210
C. 315
D. 420

Answer

To convert the angular velocity from radians per second to revolutions per minute, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given angular velocity**:
The angular velocity is given as \( \omega = 11 \, \text{radians/second} \).

2. **Understand the conversion factors**:
- One complete revolution corresponds to \( 2\pi \) radians.
- There are 60 seconds in a minute.

3. **Convert radians to revolutions**:
To convert from radians to revolutions, we can use the conversion:
\[ \text{Revolutions} = \frac{\text{Radians}}{2\pi} \]
Thus, the angular velocity in revolutions per second is:
\[ \omega_{\text{rev/s}} = \frac{11 \, \text{radians/second}}{2\pi} \]

4. **Convert revolutions per second to revolutions per minute**:
To convert revolutions per second to revolutions per minute, we multiply by 60:
\[ \omega_{\text{rev/min}} = \omega_{\text{rev/s}} \times 60 = \left(\frac{11}{2\pi}\right) \times 60 \]

5. **Simplify the expression**:
\[ \omega_{\text{rev/min}} = \frac{11 \times 60}{2\pi} = \frac{660}{2\pi} = \frac{330}{\pi} \]

6. **Substituting the value of \(\pi\)**:
Using \( \pi \approx \frac{22}{7} \):
\[ \omega_{\text{rev/min}} = \frac{330}{\frac{22}{7}} = 330 \times \frac{7}{22} \]

7. **Calculate the final value**:
\[ \omega_{\text{rev/min}} = \frac{2310}{22} = 105 \, \text{revolutions per minute} \]

### Final Answer:
The angular velocity of the flywheel in revolutions per minute is \( 105 \, \text{rev/min} \).

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