![]() This is in fact a principle in classical mechanics, known as d’Alembert’s principle, whereby, if one refers the description of a system to an accelerating reference frame, one can replace an acceleration with a force in the opposite direction. It seems that, when referred to the reference frame of Figure IV.20, there are only two forces, but when referred to the accelerating reference frame of Figure IV.21, the system can be described perfectly well by postulating the existence of a force \( ma\) pulling towards the left. To the question “But what is the agent that is causing this so-called force?” I counter with the question “What is the agent that is causing the downward force that you attribute to some mysterious ‘gravity’ ”? The plumb-bob is merely in static equilibrium under the action of three forces, one of which is a force \( ma\) towards the left. To the passenger in the car, nothing is accelerating. The passenger in the car, however, sees things rather differently (Figure IV.21.) By application of \( F = ma\) it is easily possible to find the tension in the string and the angle that the string makes with the vertical. Some would say that there are but two forces on the plumb-bob – its weight and the tension in the string – and, as a result of these, the bob is accelerating towards the right. There is a plumb-bob hanging from the roof of the car, but, because of the acceleration of the car, it is not hanging vertically. ![]() Drawing a motor car is somewhat beyond my skills. See Figure IV.20 – but forgive my limited artistic abilities. A car is accelerating at a rate \( a\) towards the right. Let’s look at an even simpler example, not even involving rotation. Yet when we drive round a corner too fast and we feel ourselves flung away from the centre of curvature of our path, the “centrifugal force” certainly feels real enough, and indeed we can solve problems referred to rotating coordinate systems as if there “really” were such a thing as “centrifugal force”. ![]() In reality, we are told, the satellite is accelerating (the centripetal acceleration) there is only one force, namely the gravitational force, which is equal to the mass times the centripetal acceleration. When a satellite orbits around Earth, it is not held in equilibrium between two equal and opposite forces, namely gravity acting towards Earth and centrifugal force acting outwards. We are usually told in elementary books that there is “no such thing” as centrifugal force.
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