The unit of angular acceleration in the SI system is

Options

A. `Nkg^(-1)`
B. `ms^(-2)`
C. `rads^(-2)`
D. `mkg^(-1)K`

Explanation

To determine the unit of angular acceleration in the SI system, we can follow these steps:

### Step-by-Step Solution

1. **Define Angular Acceleration**:
Angular acceleration (α) is defined as the rate of change of angular velocity (ω) with respect to time (t). Mathematically, it can be expressed as:
\[ \alpha = \frac{d\omega}{dt} \]

2. **Define Angular Velocity**:
Angular velocity (ω) is the rate of change of angular displacement (θ) with respect to time. It can be expressed as:
\[ \omega = \frac{d\theta}{dt} \]

3. **Identify the Unit of Angular Displacement**:
The unit of angular displacement (θ) is radians (rad).

4. **Determine the Unit of Angular Velocity**:
Since ω is the rate of change of θ with respect to time, its unit can be derived as:
\[ \text{Unit of } \omega = \frac{\text{Unit of } \theta}{\text{Unit of } t} = \frac{\text{radians}}{\text{seconds}} = \text{rad/s} \]

5. **Calculate the Unit of Angular Acceleration**:
Angular acceleration is the rate of change of angular velocity. Therefore, its unit can be derived as:
\[ \text{Unit of } \alpha = \frac{\text{Unit of } \omega}{\text{Unit of } t} = \frac{\text{rad/s}}{\text{s}} = \text{rad/s}^2 \]

6. **Final Answer**:
Therefore, the unit of angular acceleration in the SI system is:
\[ \text{radians per second squared} \quad (\text{rad/s}^2) \]

### Conclusion
The correct answer is that the unit of angular acceleration in the SI system is **radians per second squared (rad/s²)**.