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To solve this problem, we need to determine:

1. The angular velocity of the link \( \omega \) (between points L and R).
2. The velocity of point \( L \).

We know the following information:
- The velocity of point \( R \) is given as \( V_R = 1.2 \, \text{m/s} \) to the left.
- The length of the link \( LR = 2.3 \, \text{m} \).
- The angle \( \theta = 20^\circ \) between the link and the horizontal.
  
### Step 1: Angular Velocity of the Link

The velocity at point \( R \) is related to the angular velocity \( \omega \) of the link. Using the relative velocity equation for rigid body rotation:

\[
V_R = V_L + \omega \times LR
\]

Since \( V_L \) is the velocity of point \( L \) and we are not given it explicitly, we will decompose the motion:

For point \( R \), the velocity \( V_R \) is purely horizontal. For point \( L \), its velocity will have both horizontal and vertical components. However, the rotational relationship gives us the connection between the angular velocity \( \omega \) and the linear velocity at \( R \):

\[
V_R = \omega \cdot LR \cdot \sin(\theta)
\]

We can rearrange this to solve for the angular velocity \( \omega \):

\[
\omega = \frac{V_R}{LR \cdot \sin(\theta)}
\]

Substitute the values:

\[
\omega = \frac{1.2 \, \text{m/s}}{2.3 \, \text{m} \cdot \sin(20^\circ)}
\]

Now calculate \( \omega \):

\[
\omega = \frac{1.2}{2.3 \cdot 0.3420} = \frac{1.2}{0.7866} \approx 1.53 \, \text{rad/s}
\]

### Step 2: Velocity of Point \( L \)

Once we know \( \omega \), we can find the velocity of point \( L \) using the rotational relationship. The velocity at point \( L \) will be:

\[
V_L = \omega \cdot LR
\]

Substituting the values:

\[
V_L = 1.53 \, \text{rad/s} \cdot 2.3 \, \text{m} \approx 3.52 \, \text{m/s}
\]

Thus:
- The angular velocity \( \omega \) is approximately \( 1.53 \, \text{rad/s} \).
- The velocity of point \( L \) is approximately \( 3.52 \, \text{m/s} \).

Would you like a detailed breakdown of any of these steps or further clarification?

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**5 related questions:**

1. How would the angular velocity change if the velocity of point \( R \) were doubled?
2. What would happen to the velocity of point \( L \) if the angle \( \theta \) increased?
3. How can we calculate the components of the velocity of point \( L \) in the x and y directions?
4. Can the link between points \( L \) and \( R \) experience angular acceleration in this scenario?
5. How is the direction of velocity related to the angular velocity in rigid body motion?

**Tip:** Always ensure that your angle units match your trigonometric functions—radians or degrees—as this can lead to calculation errors.

Si el rodillo R de la biela inclinada se mueve a la izquierda a una velocidad constante de VR = 1,2 m/s, determine la velocidad angular del eslabón y la velocidad del rodillo L cuando el ángulo θ es igual a 20°.

Learn how to calculate the angular velocity of a link and the velocity of the rod at point L when a system moves with constant velocity and the angle is 20°. This problem uses rigid body rotation formulas and involves trigonometric functions. Suitable for students in Grades 11-12.

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