A point on the rim of a wheel 3 m in diameter has linear velocity of 18 `ms^(-1)` . The angular velocity of the wheel is

Options

A. 4 rad `s^(-1)`
B. 12 rad `s^(-1)`
C. 6 rad `s^(-1)`
D. 18 rad `s^(-1)`

Answer

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

### Step 1: Identify the given values
- The diameter of the wheel (D) = 3 m
- The linear velocity (V) = 18 m/s

### Step 2: Calculate the radius of the wheel
The radius (r) is half of the diameter. Therefore:
\[ r = \frac{D}{2} = \frac{3 \, \text{m}}{2} = 1.5 \, \text{m} \]

### Step 3: Use the formula for angular velocity
The relationship between linear velocity (V) and angular velocity (ω) is given by the formula:
\[ \omega = \frac{V}{r} \]
Where:
- ω = angular velocity (in radians per second)
- V = linear velocity (in meters per second)
- r = radius (in meters)

### Step 4: Substitute the values into the formula
Now we can substitute the known values into the formula:
\[ \omega = \frac{18 \, \text{m/s}}{1.5 \, \text{m}} \]

### Step 5: Calculate the angular velocity
Perform the division:
\[ \omega = 12 \, \text{radians/second} \]

### Conclusion
The angular velocity of the wheel is \(12 \, \text{radians/second}\).

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