The angular speed of the wheel of a vehicle is increased from 360 rpm to 1200 rpm in 14 second Its angular acceleration is

Options

A. `2pi rad/s^2`
B. `28 pi rad/s^2`
C. `120 pi rad/s^2`
D. `1 rad/s^2`

Answer

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

### Step 1: Identify the given values
- Initial angular speed (n_initial) = 360 rpm
- Final angular speed (n_final) = 1200 rpm
- Time interval (Δt) = 14 seconds

### Step 2: Convert angular speeds from rpm to rad/s
We use the formula:
\[ \omega = 2\pi \times \frac{n}{60} \]
where \( n \) is in revolutions per minute (rpm).

**For the final angular speed (n_final = 1200 rpm):**
\[ \omega_{final} = 2\pi \times \frac{1200}{60} = 2\pi \times 20 = 40\pi \, \text{rad/s} \]

**For the initial angular speed (n_initial = 360 rpm):**
\[ \omega_{initial} = 2\pi \times \frac{360}{60} = 2\pi \times 6 = 12\pi \, \text{rad/s} \]

### Step 3: Calculate the angular acceleration (α)
Angular acceleration (α) is given by the formula:
\[ \alpha = \frac{\omega_{final} - \omega_{initial}}{\Delta t} \]

Substituting the values we calculated:
\[ \alpha = \frac{40\pi - 12\pi}{14} = \frac{28\pi}{14} \]

### Step 4: Simplify the expression
\[ \alpha = 2\pi \, \text{rad/s}^2 \]

### Final Answer
The angular acceleration of the wheel is \( 2\pi \, \text{rad/s}^2 \).

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