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To solve this problem, we need to calculate the speed of the current based on the rotation speed of the paddle wheel and its radius.

### Given Data:
- Radius of the paddle wheel, \( r = 0.5 \) m
- Rotation speed, \( f = 100 \) rpm (revolutions per minute)

### Solution:
1. **Convert the rotational speed to radians per second**:
   - Since \( 1 \text{ revolution} = 2\pi \text{ radians} \),
   - \( 100 \text{ rpm} = 100 \times \frac{2\pi \text{ radians}}{1 \text{ minute}} \).
   - Convert minutes to seconds: \( 100 \times \frac{2\pi}{60} \text{ radians per second} \).

   \[
   \omega = \frac{100 \times 2\pi}{60} = \frac{100 \times 3.1416}{30} \approx 10.47 \text{ rad/s}
   \]

2. **Calculate the linear (tangential) speed at the edge of the paddle wheel**:
   - The linear speed \( v \) of a point on the edge of a rotating wheel is given by \( v = \omega \cdot r \),
   - Where \( \omega = 10.47 \) rad/s and \( r = 0.5 \) m.

   \[
   v = 10.47 \times 0.5 \approx 5.235 \text{ m/s}
   \]

### Answer:
The speed of the current is approximately **5.24 m/s**.

Would you like more details or have any further questions?

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Here are five related questions to consider:
1. How would the speed change if the paddle wheel's radius was increased?
2. What would the current speed be if the rotation rate increased to 200 rpm?
3. How does changing the radius affect the accuracy of current measurements?
4. What is the significance of converting rpm to rad/s in this calculation?
5. How would the calculation change if the paddle was partially submerged?

**Tip:** When dealing with rotational motion, always ensure units are consistent, especially converting between rpm and rad/s for accurate calculations.

To measure the speed of a current, scientists place a paddle wheel in the stream and observe the rate at which it rotates. If the paddle wheel has a radius of 0.5 m and rotates at 100 rpm, find the speed of the current in m/s.

Learn how to calculate the speed of a current based on paddle wheel rotation. Given a paddle wheel with a radius of 0.5 m rotating at 100 rpm, this problem demonstrates converting rpm to rad/s and calculating linear speed to find the current speed.

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