Explain why an object that moves round a complete circle will have an angular displacement of 2 pi radians but tangential displacement of 0 m
Full circulation has 2pi r so the angular displacement is 2pi but the tangential displacement (that came back to the inital point) have 0m magnitude
Well, it's like this - when an object moves in a complete circle, it goes all the way around and ends up at the same starting point, right? So, the angular displacement is the measure of how far it has rotated, and since it has done a full circle, the angular displacement is 2π radians.
But here's the funny part - the tangential displacement is all about how far it has moved in a straight line. And since the object ends up where it started, it hasn't actually moved anywhere in a straight line. So, the tangential displacement is 0 meters.
So, in conclusion, the object has done a complete loop-de-loop in terms of rotation but hasn't gone anywhere in terms of linear motion. It's like going on a roller coaster ride that takes you right back to where you started - lots of spinning, but no actual progress.
When an object moves in a complete circle, it undergoes both angular displacement and tangential displacement.
Angular displacement refers to the change in the object's position relative to the center of the circle it is moving in, measured in radians. A complete circle has an angular displacement of 2π radians or 360 degrees. This means that the object has gone full circle and returned to its starting position relative to the center.
On the other hand, tangential displacement refers to the change in the object's position along the circumference of the circle. In a complete circle, the object starts and ends at the same point along the circumference, resulting in zero tangential displacement.
To visualize this, imagine a point on the rim of a wheel. As the wheel rotates, the point moves in a circular path. At the start and end of the rotation, the point is at the same physical location on the rim (zero tangential displacement). However, during this time, the point has traversed the entire circumference of the circle, resulting in a complete angular displacement of 2π radians.
In summary, an object that moves around a complete circle has an angular displacement of 2π radians because it goes through a full rotation. At the same time, it has a tangential displacement of 0 meters because it starts and ends at the same point along the circumference.
When an object moves in a complete circle, it goes through a full revolution, returning to its starting point. Angular displacement measures the angle traversed by the object during its motion. In a complete circle, there are 2π radians, which is equivalent to 360 degrees. This means that the object completes a full rotational distance of 2π radians.
On the other hand, tangential displacement refers to the straight-line distance between the object's initial position and its final position. In the case of an object moving in a circle, even though it returns to its starting point, the tangential displacement is considered to be zero. This is because the net displacement in the direction of motion is zero since the object has no overall linear motion. Although the object covers a certain distance as it moves around the circle, it does not progress or move in a consistent direction along a straight line.
To calculate the angular displacement, you can use the formula:
Angular Displacement = Arc Length / Radius
Given that the circumference of a circle is 2π times its radius, the arc length in a complete circle is equal to the circumference of the circle. Therefore, the angular displacement of an object moving in a complete circle is 2π radians. However, since the object does not experience any tangential displacement, the value remains at 0 meters.