how is Octogonal path motion near to circular motion?
Answers
Answer:
When a body or an object moves in a circle, its motion is called circular motion. In other words, motion in a circle is circular motion.
When a body (or object) is moving along a circular path, then its direction of motion (or direction of speed) keeps changing continuously.
Since the velocity changes (due to continuous change in direction), therefore, the motion along a circular path is said to be accelerated.
When a body moves in a circular path with uniform speed (constant speed), its motion is called uniform circular motion.
Figure (a) shows the path of an athlete along a rectangular track PQRS. The athlete changes his direction of motion at the four corners P, Q, R, S of the rectangular track, in every round.
Figure (b) shows a hexagonal path where in every round, the direction of motion is changed at the six corners P, Q, R, S, T, U and P.
In figure (c) the track is a regular octagon. In every round, the athlete has to change the direction of motion at eight corners P, Q, R, S, T, U, V, W of the octagon; and so on. We observe that as number of sides of track increase, athlete has to take turn more and more number of times.
If we go on increasing the number of sides of the track indefinitely, we find that the shape of the track approaches the shape of a circle. The length of each side tends to be zero.
Along the circle, the athlete has to change his direction of motion at each point.
Therefore, the effective direction of motion is along the tangent to the circular path at that point as shown in figure (d).