A belt passes over a wheel of radius 25 cm. If a point on the belt has a speed of `5m//s`, the belt is moving with an angular velocity of

Options

A. `3.2 rad //s`
B. `0.32 rad//s`
C. `20 rad//s`
D. `0.032 rad//s`

Explanation

To find the angular velocity of the belt moving over a wheel, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Radius of the wheel (r) = 25 cm = 0.25 m (convert to meters for consistency)
- Speed of the point on the belt (v) = 5 m/s

2. **Use the Relationship Between Linear Speed and Angular Velocity:**
The relationship between linear speed (v) and angular velocity (ω) is given by the formula:
\[ v = \omega \cdot r \]
where:
- \( v \) is the linear speed,
- \( \omega \) is the angular velocity in radians per second,
- \( r \) is the radius of the wheel.

3. **Rearrange the Formula to Solve for Angular Velocity (ω):**
To find the angular velocity, we can rearrange the formula:
\[ \omega = \frac{v}{r} \]

4. **Substitute the Known Values into the Equation:**
Now, substitute the values of \( v \) and \( r \):
\[ \omega = \frac{5 \, \text{m/s}}{0.25 \, \text{m}} \]

5. **Calculate the Angular Velocity:**
\[ \omega = \frac{5}{0.25} = 20 \, \text{radians/second} \]

### Final Answer:
The angular velocity of the belt is \( \omega = 20 \, \text{radians/second} \).