explain why an object that moves round a complete circle will have an angular displacement of 2pi radians but displacement of 0m.
distance is a scalar and the distance is indeed 2 pi R
HOWEVER displacement is a VECTOR and has both magnitude and direction from the starting point to the finish point.
In this case the magnitude of displacement from the start to the finish is ZERO. Your angular direction never changed sign. If you went around the circle then came back, the story would be different :)
An object that moves around a complete circle will have an angular displacement of 2π radians but a displacement of 0 meters. Let's break down the explanation step-by-step:
1. Angular Displacement: Angular displacement refers to the angle through which an object has rotated or moved around a circular path. In a complete circle, there are 360 degrees or 2π radians. Therefore, a full revolution around a circle corresponds to an angular displacement of 2π radians.
2. Displacement: Displacement, on the other hand, refers to the change in position of an object. It is a vector quantity that indicates the straight-line distance and direction from the initial position to the final position.
3. Circular Motion: When an object moves in a circular path, its position changes continuously, and it follows a curved trajectory. However, during a complete circular motion, the object returns to its initial position. As a result, the overall change in position is zero, indicating that the displacement is 0 meters.
4. Recap: To summarize, the angular displacement of an object moving around a complete circle is 2π radians because it completes one full revolution. However, the displacement is 0 meters because the object returns to its starting point, resulting in no net change in position.
Remember, angular displacement measures the angle covered, while displacement measures the change in position.
When an object moves around a complete circle and returns to its starting point, it has completed one revolution. In terms of angular displacement, which measures the angle covered during its motion, a complete circle covers an angle of 2π radians (or 360 degrees).
However, in terms of displacement, which measures the change in position, the object returns to its original position. Displacement is a vector quantity that requires both magnitude and direction, and since the object returns to the same position, the displacement is zero meters or any other unit of length.
To visualize this, imagine standing in one spot and taking a few steps forward, then a few steps backward. Your angular displacement is the total angle covered during your movement, but your displacement in terms of position will be zero because you return to your original position. The same principle applies to an object moving in a complete circle.