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 1: Identify the diameter and calculate the radius
The diameter of the wheel is given as 4 meters. The radius (R) is half of the diameter.

\[ R = \frac{\text{Diameter}}{2} = \frac{4 \, \text{m}}{2} = 2 \, \text{m} \]

### Step 2: Use the formula for linear velocity
The relationship between linear velocity (V) and angular velocity (ω) is given by the formula:

\[ V = \omega \times R \]

Where:
- \( V \) is the linear velocity,
- \( \omega \) is the angular velocity,
- \( R \) is the radius.

### Step 3: Rearrange the formula to solve for angular velocity
We can rearrange the formula to find angular velocity (ω):

\[ \omega = \frac{V}{R} \]

### Step 4: Substitute the known values
We know the linear velocity \( V = 16 \, \text{m/s} \) and the radius \( R = 2 \, \text{m} \). Substituting these values into the equation gives:

\[ \omega = \frac{16 \, \text{m/s}}{2 \, \text{m}} = 8 \, \text{rad/s} \]

### Step 5: Conclusion
The angular velocity of the wheel is \( 8 \, \text{rad/s} \).

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