A wheel starts from rest and acquires an angular velocity of `60 rad//s` in half a minute . Then its angular acceleration is

Options

A. `4 rad//s^(2)`
B. `2 rad//s^(2)`
C. `1 rad//s^(2)`
D. `0.5 rad//s^(2)`

Explanation

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. Let's break down the steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Initial angular velocity, \( \omega_0 = 0 \, \text{rad/s} \) (the wheel starts from rest)
- Final angular velocity, \( \omega = 60 \, \text{rad/s} \)
- Time taken, \( t = 30 \, \text{seconds} \) (half a minute)

2. **Write the formula for angular acceleration:**
The formula that relates angular acceleration (\( \alpha \)), initial angular velocity (\( \omega_0 \)), final angular velocity (\( \omega \)), and time (\( t \)) is:
\[ \omega = \omega_0 + \alpha t \]

3. **Rearrange the formula to solve for angular acceleration (\( \alpha \)):**
\[ \alpha = \frac{\omega - \omega_0}{t} \]

4. **Substitute the known values into the equation:**
\[ \alpha = \frac{60 \, \text{rad/s} - 0 \, \text{rad/s}}{30 \, \text{s}} = \frac{60 \, \text{rad/s}}{30 \, \text{s}} \]

5. **Calculate the angular acceleration:**
\[ \alpha = 2 \, \text{rad/s}^2 \]

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

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

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