A mark on the rim of a rotating cicular wheel of 0.50 m radius is moving with a speed of `10 ms^(-1)` . Find its angular speed.

Answer

To find the angular speed of a mark on the rim of a rotating circular wheel, we can use the relationship between linear speed (v) and angular speed (ω). The formula that relates these two quantities is:

\[ v = \omega \times r \]

Where:
- \( v \) is the linear speed,
- \( \omega \) is the angular speed,
- \( r \) is the radius of the circular wheel.

### Step-by-Step Solution:

1. **Identify the given values**:
- Radius of the wheel, \( r = 0.50 \, \text{m} \)
- Linear speed, \( v = 10 \, \text{m/s} \)

2. **Use the formula to find angular speed**:
We rearrange the formula to solve for angular speed \( \omega \):
\[ \omega = \frac{v}{r} \]

3. **Substitute the values into the formula**:
\[ \omega = \frac{10 \, \text{m/s}}{0.50 \, \text{m}} \]

4. **Calculate the angular speed**:
\[ \omega = \frac{10}{0.50} = 20 \, \text{rad/s} \]

5. **Conclusion**:
The angular speed of the mark on the rim of the rotating wheel is \( 20 \, \text{rad/s} \).