What is the displacement of point P when a wheel turns half time forward? R = 4m

When a wheel turns half a revolution (or half a turn) forward, the displacement of a point on the rim of the wheel can be determined by considering the distance it moves.

### Given:
- Radius of the wheel \( R = 4 \, \text{m} \)

### Displacement of Point P:
1. **Circumference of the Wheel**: The distance around the entire wheel is given by the formula:
   \[
   \text{Circumference} = 2\pi R = 2\pi \times 4 \, \text{m} = 8\pi \, \text{m}
   \]
2. **Distance Point P Travels in Half a Turn**: Since the wheel turns half a revolution:
   \[
   \text{Distance traveled by Point P} = \frac{1}{2} \times 8\pi \, \text{m} = 4\pi \, \text{m}
   \]
3. **Displacement**: Displacement is the shortest distance between the initial and final positions of Point P. In a half-turn, Point P moves from its initial position to the diametrically opposite point on the wheel. The displacement is equal to the diameter of the wheel:
   \[
   \text{Displacement} = 2R = 2 \times 4 \, \text{m} = 8 \, \text{m}
   \]

### Conclusion:
The displacement of Point P when the wheel turns half a revolution forward is **8 meters**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What would be the displacement if the wheel turned a full revolution?
2. How is displacement different from the distance traveled in circular motion?
3. What is the displacement after a quarter turn of the wheel?
4. How would the displacement change if the radius were doubled?
5. How can this problem be extended to calculate the velocity of Point P?

**Tip:** Remember that displacement is a vector quantity, meaning it has both magnitude and direction, while distance is a scalar quantity and only has magnitude.

Explore how to calculate the displacement of Point P on a wheel with radius R = 4m when it turns half a revolution forward. Understand the relationship between circular motion, displacement, and the geometry of circles. Suitable for Grades 7-9 students.

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