A wheel of radius 0.5 m rotates with a constant angular speed about an axis perpendicular to its center. A point on the wheel that is 0.2 m from the center has a tangential speed of 2 m/s.
Determine the tangential speed of a point 0.4 m from the center of the wheel.

Options

A. 0.4 m/s
B. 4 m/s
C. 2 m/s
D. 10 m/s

Answer

To solve the problem, we will use the relationship between tangential speed (V), radius (R), and angular speed (ω) of a rotating wheel. The key relationship is given by:

\[ V = R \cdot \omega \]

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Radius of the wheel (R) = 0.5 m (not directly needed for the calculation).
- Distance from the center for the first point (R1) = 0.2 m.
- Tangential speed at this point (V1) = 2 m/s.
- Distance from the center for the second point (R2) = 0.4 m.

2. **Calculate Angular Speed (ω)**:
Using the first point's tangential speed, we can find the angular speed (ω):
\[ V1 = R1 \cdot \omega \implies \omega = \frac{V1}{R1} \]
Substituting the known values:
\[ \omega = \frac{2 \, \text{m/s}}{0.2 \, \text{m}} = 10 \, \text{rad/s} \]

3. **Determine the Tangential Speed at the Second Point**:
Now, we can find the tangential speed (V2) at the second point (0.4 m from the center):
\[ V2 = R2 \cdot \omega \]
Substituting the values:
\[ V2 = 0.4 \, \text{m} \cdot 10 \, \text{rad/s} = 4 \, \text{m/s} \]

4. **Final Answer**:
The tangential speed of a point 0.4 m from the center of the wheel is:
\[ V2 = 4 \, \text{m/s} \]