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Understanding Pseudo-force

In my discussion on the Newton's Laws, I had stated that there are frames called Inertial Frames where the Newton's Laws are valid. No frame is absolutely inertial (there was a time when people used to think of a frame which is absolutely inertial, called the ether frame, the existence of which was finally proved wrong, as we shall see in our discussion on Michelson-Morley's experiment). For example, we live on the earth, and we consider the earth to be an inertial frame, and every frame in uniform motion with respect to the earth is considered inertial. However whatever we see in the earth's atmosphere e.g. winds deviating from their actual course instead of the fact that no force acts on them, etc. which are actually due to the earth's rotation, prove that the earth frame is actually accelerated (rotating) with respect to an outside frame (say the sun frame). Thus we see, whenever we see that in some frame there has been no deviation from the Newton's Laws till date, we say that the frame is most probably an inertial one, and consider all frames in uniform motion with respect to that frame to be inertial. But if there occurs a single deviation from the Newton's Laws in the original frame, then the frame can no longer be considered an inertial frame, and is called a non-inertial one, and each and every frame described before to be in uniform motion with respect to it becomes a non-inertial one. Non-inertial frames mean simply those ones, where there can be an acceleration without a force. Suppose a train moves with uniform velocity with respect to the earth (the earth frame can be justifiably considered an inertial frame for the study of phenomena occurring on the surface of the earth). A group of players is playing snooker on a snooker-board inside the train and the snooker balls are following the Newton's Laws perfectly, the train being an inertial frame (since it is in uniform motion with respect to the earth). However, when the train suddenly decelerates to rest, the validity of the laws are no longer preserved, and the balls deviate from their paths in weird directions without any real force acting on them. So in order to justify such no-force accelerations in those frames, one can bring the concept of pseudo-forces or imaginary forces which one can then hold responsible for such uncanny accelerations. This in turn converts the non-inertial frame into a pseudo-inertial frame, where the Newton's Laws can then be applied. Suppose a person is rotating and his friend is observing him from the ground. The friend sees that the person has a centripetal force (say friction) acting on him, which makes him rotate, by tethering him to the center of rotation. If the friction is not enough to make the person rotate with the given velocity and at the given radius from the center, the person will simply get thrown away tangentially (since the ground frame is inertial,according to the Newton's Laws the person who is rotating has a natural tendency, in such a frame, to move in a straight line with uniform speed, which is the tangent here, if such tethering force is absent, or inadequate). The friction, which tries to oppose such a tangential motion, acts inwards and provides the necessary centripetal force for rotation. But if the same situation is observed by the person himself, he will feel some force pulling him constantly towards a fixed point (the center), but he will not find himself in motion (he himself being in the rotating frame). Thus, he may argue using the Newton's Laws that some force must be pulling him outwards to keep him at rest, though no such real force exists. Thus, in order to make the equation of motion valid in the rotating frame also, he brings the concept of an imaginary force or pseudo-force, that he imagines to pull him always outwards from the fixed point. This force, he calls the "centrifugal force". Similar is the concept of what we call the Coriolis Force, named after G.G. Coriolis. Suppose, two little girls A and B are sitting at the antipodes (the diametrically opposite seats) of a merry-go-round and are playing an interesting game where A throws a ball and B has to catch it, and vice versa. We consider the frame of A. A sees B to be sitting right in front of her, opposite to her on the merry-go-round, and B's position is constant with respect to A throughout the motion. However, when A throws the ball to B along the vertical plane containing A and B, or in other words, along the straight line joining A and B, the ball is never expected to reach B, as in that interval of time, B already gets displaced to a new position, due to the rotation of the frame. However, what A sees is that when she throws the ball, it instead of tracing out a parabola in the vertical plane, suddenly deviates away from the vertical plane, and never reaches B whom A sees to be sitting at the same position in front of her. So in order to make the ball reach B, A has to throw it making some angle with the vertical plane. Thus A sees the ball deviating from the vertical plane, without the presence of some real force. So she brings the concept of an imaginary force or pseudo-force, called the "Coriolis Force". This she holds responsible for such deviation (which is an acceleration) of the ball. Same concept applies in case of drift of Planetary Winds also. The planetary winds (the Trades, the Westerlies, and the Polars) are expected to blow either from north to south, or from south to north. But as the earth's atmosphere is loosely bound to the earth's surface, and the atmosphere's rotational speed is less than the earth's one, we see the winds deviating from their expected course, somewhat towards east or west (as given by the working rules like the Ferrel's Law, or the Buys-Ballot's Law). The reason is the same Coriolis Force.

Note by Kuldeep Guha Mazumder
1 year, 3 months ago

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