A point in the rim of a wheel 4 m in diameter has linear velocity of `16 ms ^(-1) ` The angular velocity of wheel is

Options

A. ` 4 rad s^(-1)`
B. ` 8 rad s ^(-1)`
C. ` 12 sin 40^@`
D. ` 20 rad s^(-1)`

Explanation

To find the angular velocity of the wheel, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Diameter of the wheel = 4 m
- Linear velocity (v) = 16 m/s

2. **Calculate the Radius of the Wheel**:
- The radius (r) is half of the diameter.
\[ r = \frac{\text{Diameter}}{2} = \frac{4 \, \text{m}}{2} = 2 \, \text{m} \]

3. **Use the Relationship Between Linear Velocity and Angular Velocity**:
- The relationship between linear velocity (v) and angular velocity (ω) is given by the formula:
\[ v = \omega \cdot r \]
Rearranging this formula to find angular velocity (ω):
\[ \omega = \frac{v}{r} \]

4. **Substitute the Known Values into the Formula**:
- Substitute the values of v and r into the equation:
\[ \omega = \frac{16 \, \text{m/s}}{2 \, \text{m}} = 8 \, \text{radians/s} \]

5. **Conclusion**:
- The angular velocity of the wheel is:
\[ \omega = 8 \, \text{radians/s} \]

### Final Answer:
The angular velocity of the wheel is \(8 \, \text{radians/s}\).

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