A dust particle lying at the rim of a wheel has an angular speed of 22 rad/s. Find the time period.

Answer

To solve the problem of finding the time period of a dust particle lying at the rim of a wheel with an angular speed of 22 rad/s, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The time period \( T \) of an object in circular motion is related to its angular speed \( \omega \) by the formula:
\[ T = \frac{2\pi}{\omega} \]

2. **Identify Given Values**: From the problem, we know:
- Angular speed \( \omega = 22 \, \text{rad/s} \)

3. **Substitute the Value into the Formula**: Plug the value of angular speed into the formula for time period:
\[ T = \frac{2\pi}{22} \]

4. **Calculate \( 2\pi \)**: We can use the approximation \( \pi \approx \frac{22}{7} \):
\[ 2\pi \approx 2 \times \frac{22}{7} = \frac{44}{7} \]

5. **Calculate the Time Period**: Now substitute this back into the equation for \( T \):
\[ T = \frac{\frac{44}{7}}{22} \]
Simplifying this gives:
\[ T = \frac{44}{7 \times 22} = \frac{44}{154} = \frac{2}{7} \, \text{seconds} \]

6. **Final Answer**: Therefore, the time period \( T \) is:
\[ T = \frac{2}{7} \, \text{seconds} \]

### Summary:
The time period of the dust particle is \( \frac{2}{7} \) seconds.

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