Question

How much is the displacement in one cycle of a circular motion?

Answer 1

Displacement is the shortest distance between two points, i.e., between the starting point and the ending point. It is independent of the path taken by an object. The circle after one cycle has the same starting and ending point.

Complete answer:
We know from our previous knowledge of mechanics that displacement is defined as the shortest distance between two points between which an object has undergone a motion. It is a vector quantity pointing from the initial position of a body to its final position. An object can take any path between two points A and B, the distance covered by it, is the total path covered by the body in moving from A to B via the given path, whereas the displacement is the straight line connecting the two points A and B.

From the above discussion, it is clear that the displacement is the shortest distance a body can undergo from two given points. Also, it is always a straight line.
Now, let us consider the circular motion a body undergoes.

It is given that a cycle of a circular motion is considered. We know that, one cycle of a circular motion is the motion of an object from a point A on the circle to the same point A after a complete revolution.
Obviously, in this case of circular motion the initial point and the final point are the same. From the definition, it is clear that displacement to be considered is in between only one point, which turns out to be zero.

Therefore, we can come to the conclusion that the displacement in one cycle of a circular motion is zero.

Additional Information:
The displacement involved for ‘n’ number of cycles of circular motion, given that n is an integer, is always zero. Also, the half cycles in a circular motion gives the magnitude of displacement equal to the diameter of the circle.

Note:
The distance and displacement are often mistreated by the students. Extreme care should be taken while solving problems regarding the displacement as it involves both magnitude and direction. In a circular motion, angular displacement also comes to play, which is the angle measure and will be 360 degrees for one cycle.