What is the SI unit of angular velocity is ________

Options

A. `"Hertz"^(-1)`
B. Sm
C. rad `s^(-1)`
D. `Sm ^(-5)`

Explanation

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

### Step 1: Understand the definition of angular velocity
Angular velocity (ω) is defined as the rate of change of angular displacement (θ) with respect to time (t). Mathematically, it can be expressed as:
\[ \omega = \frac{\theta}{t} \]

### Step 2: Identify the SI units involved
- The SI unit of angular displacement (θ) is **radian**.
- The SI unit of time (t) is **second**.

### Step 3: Combine the units to find the SI unit of angular velocity
From the definition, we can substitute the SI units into the equation:
\[ \text{SI unit of } \omega = \frac{\text{radian}}{\text{second}} = \text{radian per second} \]

### Step 4: Conclusion
Thus, the SI unit of angular velocity is:
\[ \text{radian per second} \]

### Final Answer
The SI unit of angular velocity is **radian per second**.

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