Why do we need fictitious forces?
By Quamrul Haider
While we can answer this question using complicated equations and confusing scientific jargon, theres a simpler way to understand the necessity of fictitious forces. Suppose you and a friend stood on a merry-go-round playing catch, with you near the center and your friend close to the edge. If the merry-go-round remains stationary, then a ball thrown by you towards your friend would travel in a straight line.
If you throw the ball straight across while the merry-go-round rotates rapidly in the counterclockwise direction, the ball would appear to veer to the right. You would think that a mysterious force pushed the ball to the right. But a person watching the throw from the sideline will see the ball travel in a straight line.
The reason for the mysterious force has to do with the frame of reference from where you observed the phenomenon. A reference frame is a framework consisting of a coordinate system to locate the position of an object in space and a clock assigning times at positions with respect to the coordinate system. The reference frame in which observers are stationary or moving with constant velocity is called an inertial frame. Insofar as laws of motion are concerned, they are the same in all inertial frames. By contrast, a noninertial reference frame is one in which the observers are undergoing acceleration. In such a frame, the laws of motion appear to be violated. Hence, to explain the motion of objects from a noninertial frame, fictitious forces must be introduced.
A rotating reference frame is noninertial because objects moving in a circle, like you on the merry-go-round, experience acceleration called centripetal acceleration directed towards the center of the circle. Since the Earth rotates counterclockwise about its axis, an observer on Earths surface also has centripetal acceleration. A reference frame fixed to the Earth is, therefore, noninertial.
One of the fictitious forces that we have to invoke in order to describe motion viewed from a rotating reference frame is called Coriolis force. Its effects were discovered by the nineteenth century French engineer Gaspard Coriolis. The effect, known as Coriolis Effect, is an apparent deflection of the path of an object moving in a noninertial system.
Thus, the mysterious force that pushed your ball to the right is the fictitious Coriolis force. To offset the deflection so that your friend can catch the ball, you would have to throw it towards the point where he/she will be in a few moments.
During a flight from London to Dhaka, if deflection due to Coriolis force is ignored, the aircraft would be off course, albeit slightly in the southerly direction. The deflection will be significant on long haul flights lasting 15 to 20 hours. There will be no deflection if the aircraft flies along the equator. The aircraft would experience the most deflection near the poles.
The most important influence of Coriolis force on aircrafts, however, is due to the effect the force has on the direction of the jet stream. When pilots make correction for the winds, the deflection due to Coriolis force is automatically corrected.
Coriolis force deflects anything flying or flowing along the longitudinal line - northward or southward - to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. The amount of deflection varies with latitude and speed of the object. It is greatest at the poles and decreases as we approach the equator. It is exactly zero at the equator. Coriolis Effect increases as the speed of the object increases, but is inconsequential if the object is lighter.
For objects falling vertically downward, the deflection is eastward in the Northern Hemisphere and westward in the Southern Hemisphere. Maximum deflection occurs at the equator; it is zero at the poles.
Coriolis Effect plays a major role in military operations. During World War I, the Germans had to compensate for the Earths rotation as they fired shells at Paris with a howitzer that they called Big Bertha. If they hadnt taken Coriolis Effect into account, their shells, which were fired from 70 miles away, would have missed the target by a large distance.
Coriolis force is part of the reason why hurricanes in the Northern Hemisphere rotate counterclockwise. Rather than flowing directly from areas of high pressure to low pressure, as they would on a non-rotating planet, the force causes the wind at mid-latitudes to circulate counterclockwise north of the equator and clockwise south of the equator. Tornadoes on the other hand are not impacted by Coriolis force because they are small in scale and short in duration.
Although Coriolis force is useful in describing many physical phenomena, it is not a real force. Its an artifact that enables us to look at the world from a noninertial frame of reference. In reality, the deflection occurs because of the Earths eastward rotational motion and its differing tangential speeds at various latitudes.
The flamboyant Nobel physicist Richard Feynman once asked the following question but did not give an answer: Is gravity a fictitious force? The answer can be found in Einsteins general relativity theory whose cornerstone is the proposition that gravity, which we know as a real force, is a fictitious force because it is a manifestation of the curvature of the fabric of space and time.
Did Einstein blur forever the distinction between real and fictitious forces? Not necessarily. When the gravitating objects are huge and the distortion of spacetime is large, gravity is indeed a fictitious force. For small-sized objects, curvature of spacetime is small and gravity is a real force.
The writer is Professor of Physics at Fordham University, New York.
Photo: Google Image
