A wheel starts rotating at 10 rad/sec and attains the angular velocity of 100 rad/sec in 15 seconds. What is the angular acceleration in rad/`sec^(2)`? `

Options

A. 10
B. `110//15`
C. `100//15`
D. 6

Answer

To find the angular acceleration of the wheel, we can use the formula for angular acceleration, which relates the initial angular velocity, final angular velocity, and time taken for the change in angular velocity. The formula is:

\[ \alpha = \frac{\omega_f - \omega_i}{t} \]

Where:
- \(\alpha\) = angular acceleration (in rad/s²)
- \(\omega_f\) = final angular velocity (in rad/s)
- \(\omega_i\) = initial angular velocity (in rad/s)
- \(t\) = time taken for the change (in seconds)

### Step-by-Step Solution:

1. **Identify the given values:**
- Initial angular velocity, \(\omega_i = 10 \, \text{rad/s}\)
- Final angular velocity, \(\omega_f = 100 \, \text{rad/s}\)
- Time taken, \(t = 15 \, \text{s}\)

2. **Substitute the values into the formula:**
\[ \alpha = \frac{100 \, \text{rad/s} - 10 \, \text{rad/s}}{15 \, \text{s}} \]

3. **Calculate the difference in angular velocities:**
\[ \alpha = \frac{90 \, \text{rad/s}}{15 \, \text{s}} \]

4. **Perform the division:**
\[ \alpha = 6 \, \text{rad/s}^2 \]

5. **Conclusion:**
The angular acceleration of the wheel is \(6 \, \text{rad/s}^2\).