A particle goes uniformly in circular motion with an angualr speed `pi/8 rad s^(-1)` . What is its time period ?

Answer

To find the time period of a particle undergoing uniform circular motion, we can use the relationship between the time period (T) and the angular speed (ω). The formula for the time period is given by:

\[ T = \frac{2\pi}{\omega} \]

### Step-by-Step Solution:

1. **Identify the given values**:
- The angular speed (ω) is given as \( \frac{\pi}{8} \) rad/s.

2. **Substitute the value of angular speed into the formula**:
\[ T = \frac{2\pi}{\frac{\pi}{8}} \]

3. **Simplify the expression**:
- To divide by a fraction, we multiply by its reciprocal:
\[ T = 2\pi \times \frac{8}{\pi} \]

4. **Cancel out π**:
\[ T = 2 \times 8 = 16 \text{ seconds} \]

5. **Conclusion**:
- The time period \( T \) for the particle in uniform circular motion is \( 16 \) seconds.

### Final Answer:
The time period is **16 seconds**.