Understanding the Concept
* Rotation: When a wheel rolls, the point initially in contact with the ground traces a path called a cycloid.
* Displacement: Displacement is the straight-line distance between the initial and final positions of an object.
Calculations
1. Half Revolution: A half revolution means the wheel has rotated 180 degrees.
2. Arc Length: The point initially in contact with the ground travels along the circumference of the wheel. The distance it travels in a half revolution is half the circumference:
* Arc Length = (1/2) * 2πR = πR
3. Final Position: After a half revolution, the point is at the top of the wheel, directly above its starting position.
4. Displacement: The displacement is the straight-line distance between the initial and final positions. This is simply the diameter of the wheel:
* Displacement = 2R
Therefore, the displacement of the point initially in contact with the ground when the wheel rolls forward one-half revolution is 2R.
