https://file.aiquickdraw.com/mathbot/file/1725994612118gytmq66w.jpg

The image provided is in French and illustrates a car turning around a bend, focusing on the calculation of the rotational speed of the inner wheel of the car. Here is a breakdown of the relevant information from the image:

### Given Information:
1. **Rayon du virage (Turn radius)**: \( R = 23 \, \text{m} \)
2. **Vitesse linéaire de la voiture (Linear speed of the car)**: 
   - \( V = 54 \, \text{km/h} = 15 \, \text{m/s} \)
3. **Rayon intérieur et extérieur (Inner and outer radius)**: 
   - \( R_i = 22.3 \, \text{m} \)
   - \( R_e = 23.7 \, \text{m} \)
4. **Vitesse de la voiture par rapport au sol (Speed of the car relative to the ground)**:
   - \( V_e = 14.2 \, \text{m/s} \) (outer wheel)
   - \( V_i = 13.3 \, \text{m/s} \) (inner wheel)
5. **Rayon de la roue (Wheel radius)**: \( r = 27 \, \text{cm} = 0.27 \, \text{m} \)
6. **Vitesse de rotation (Rotational speed)**:
   - \( \omega = 0.6 \, \text{rad/s} = 5.7 \, \text{trs/min} \)

### Objective:
- To calculate the **vitesse de rotation de la roue intérieure (rotational speed of the inner wheel in rad/s)**.

### Calculation:
The rotational speed of the wheel can be found using the relationship between the linear speed of the inner wheel (\(V_i\)) and its radius (\(r\)):

\[
\omega_i = \frac{V_i}{r}
\]

Substituting the given values:

\[
\omega_i = \frac{13.3 \, \text{m/s}}{0.27 \, \text{m}}
\]

Let's calculate the value:The rotational speed of the inner wheel is approximately \(49.26 \, \text{rad/s}\).

Would you like more details on this calculation or have any questions?

### Related Questions:
1. How is the rotational speed affected by the wheel's radius?
2. What would be the rotational speed if the outer wheel's speed is used instead?
3. How would the rotational speed change if the turn radius \(R\) were different?
4. Can we calculate the centripetal force acting on the car?
5. How is angular velocity related to linear velocity in circular motion?

**Tip:** Always ensure to convert all units to the SI system (meters, seconds, radians) before performing calculations for consistency and accuracy.

Calculate the rotational speed of the inner wheel of a car turning around a bend.

Learn how to calculate the rotational speed of a car's inner wheel while turning. This problem involves concepts of circular motion and rotational kinematics, using the formula ω = V/r to determine the rotational speed. Suitable for high school physics students.

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