The angualr displacement of an object having uniform cirular motion is ` pi/4` rad in every 3s. Find its frequency of revolution.

Answer

To solve the problem, we need to find the frequency of revolution of an object in uniform circular motion given its angular displacement and the time taken for that displacement.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Angular displacement (θ) = π/4 radians
- Time (t) = 3 seconds

2. **Calculate Angular Velocity (ω):**
- Angular velocity (ω) is defined as the angular displacement divided by the time taken.
- Formula:
\[ \omega = \frac{\theta}{t} \]
- Substituting the values:
\[ \omega = \frac{\pi/4}{3} = \frac{\pi}{12} \text{ radians/second} \]

3. **Relate Angular Velocity to Frequency:**
- The relationship between angular velocity (ω) and frequency (f) is given by:
\[ \omega = 2\pi f \]
- Rearranging the formula to find frequency:
\[ f = \frac{\omega}{2\pi} \]

4. **Substitute the Value of Angular Velocity:**
- Now, substitute the value of ω we calculated:
\[ f = \frac{\pi/12}{2\pi} \]
- Simplifying this:
\[ f = \frac{\pi}{12} \cdot \frac{1}{2\pi} = \frac{1}{24} \text{ Hz} \]

5. **Final Answer:**
- The frequency of revolution is:
\[ f = \frac{1}{24} \text{ Hz} \]