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

Answer

To find 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 1: Understand the relationship between angular speed and time period
The angular speed (ω) is related to the time period (T) by the formula:
\[ T = \frac{2\pi}{\omega} \]
where:
- \(T\) is the time period,
- \(\omega\) is the angular speed in radians per second.

### Step 2: Substitute the given value of angular speed
We are given that the angular speed \(\omega\) is 22 rad/s. We will substitute this value into the formula:
\[ T = \frac{2\pi}{22} \]

### Step 3: Simplify the expression
Now, we can simplify the expression:
\[ T = \frac{2\pi}{22} = \frac{\pi}{11} \text{ seconds} \]

### Step 4: Calculate the numerical value
To get a numerical value, we can use the approximation \(\pi \approx 3.14\):
\[ T \approx \frac{3.14}{11} \approx 0.285 \text{ seconds} \]

### Final Answer
Thus, the time period of the dust particle is approximately:
\[ T \approx 0.285 \text{ seconds} \]

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