I was reading an article that rotation instead of linear motion is absolute. Can anyone explain why? Shouldn't an observer (A) moving in a circle around a point in an object that rotates (with respect to another observer B) consider the object stationary? Or he would feel a force which would imply accelaration?
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asked Jan 20, 2019 at 4:06
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3$\begingroup$ Can you edit your question to include a link to the article you were reading? $\endgroup$– rob ♦Commented Jan 20, 2019 at 4:09
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$\begingroup$ I don’t think so, for example two body are connect with hinge joint together, die rotation is relative $\endgroup$– EliCommented Jan 20, 2019 at 8:36
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$\begingroup$ More on Mach's principle. $\endgroup$– Qmechanic ♦Commented Jan 20, 2019 at 12:43
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2$\begingroup$ Possible duplicate physics.stackexchange.com/q/442948 $\endgroup$– Daddy KropotkinCommented Jan 20, 2019 at 14:21
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4 Answers
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I think firstly we need to distinguish between forced circular motion and circular motion around a massive body along a geodesic path.
Rotation around a point is possible by a centripetal force, for example a string, connecting the center of rotation with the moving body. In any case the body experience a centrifugal force, regardless of whether the centre rotates with the same angular velocity or not. BTW, the center as a point is a geometric imagination only, in reality the center is a body too with an outer distance to the center and undergoes also the centrifugal force.
Is rotation absolute?
The angular velocity (angle travelled per time unit or the reciprocal value revolutions per time uniti) of any point of a rotating body is the same in any distance (radius) from the center of rotation. So for this value the rotation is absolute. But the centrifugal force is a function of the distance from the center and is not a constant.
Shouldn't an observer (A) moving in a circle around a point in an object that rotates (with respect to another observer B) consider the object stationary? Or he would feel a force which would imply accelaration ?
There is a case in which a rotating around a center object indeed will not feel a centrifugal force. In free space a moving around a massive body object follows a geodesic path in a gravitational potential. For example the earth rotates in 24 h once, but the ISS rotates in 90 min around the earth. And in greater distance a satellite could rotate in 24 h with the earth. In both cases you as the astronaut does not feel any forces. But from the rotational difference between earth and the space capsule you may calculate the distance to earth.
answered Jan 20, 2019 at 7:38
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This was the basis of an important experiment by Newton where he showed that rotational movement was absolute compared to translational movement that is not, this is his famous bucket experiment.
Essentially, we can say when a rotating system is absolutely at rest, that is without reference to anything outside of it; whereas a system moving translationally we can say only when it is at rest with some other system, that is only relationally.
Mach argued, however, that rotational movement was relative; and this is the basis of Machs Principle which was an important consideration for Einstein when he developed GR; though it's arguable to what extent GR is Machian.
answered Jan 20, 2019 at 8:04
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$\begingroup$ Newton did argue that rotation is absolute, but in his reasoning he presented an observation from everyday life and a thought experiment, and not an actual experiment. The confusion may have arisen because in general Newton did perform numerous careful experiments to verify suppositions, such as his efforts to see if there was any case where inertial mass is not equivalent to gravitational mass. The case of rotation being absolute was as strong in Newton's time as it is now hence for the reasoning everyday observation is sufficient. $\endgroup$– CleonisCommented Jan 20, 2019 at 12:27
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$\begingroup$ Historians of science describe that what is referred to as 'Mach's principle' was first introduced by Einstein. Mach's philosophy of science prescribed a very austere attitude, and a statement as sweeping as Einstein's "Mach's principle" is incompatible with Mach's philosophy of science. Einstein did reference a book by Ernst Mach about mechanics. It would appear the thought occurred to Einstein while reading Mach.Historians of science have firmly established that Mach never argued for what Einstein referred to as "Mach's principle" $\endgroup$– CleonisCommented Jan 20, 2019 at 12:29
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Let me combine my answer with a bit of history of science.
In his book 'Philosophiæ Naturalis Principia Mathematica' (for short: 'the Principia'), Newton argued that rotation is absolute. Newton used two lines of reasoning, one based on an everyday observation, and one based on a thought experiment.
The everyday observation:
Think of a bucket half-filled with water. When the water is circulating the surface of the water is concave, when the water is not circulating the surface is flat. The determining factor is whether the water is in circulating motion with respect to the overall environment. The bucket itself is closest to the water, but when you discount the effects from friction the state of motion of the bucket does not determine whether the surface of the water will be flat or concave.
The thought experiment:
Imagine two objects, at some measurable distance relative to each other. Imagine they are surrounded by empty space, there is no visible reference for motion. Question: are the two objects stationary, or are they in a state of circumnavigating their common center of mass? Newton argued the answer is obvious: if there is nothing connecting the two objects and their relative distance remains the same then they are not circumnavigating. For the two objects to be circumnavitating a centripetal force must be provided; a rope or string of whatever material must be present in order to provide the required centripetal force. Given the amount of inertial mass of each object you can infer the rotation rate from a measurement of the amount of tension of the rope.
The astronomer de Sitter (1873-1934) offered the following observation/reasoning:
When two celestial bodies orbit their common center of mass in an elliptical orbit then the following characteristics remain the same: the plane of the orbit keeps the same orientation (just as with circular orbits), and the ellipse keeps pointing in the same direction. That is, unless influenced by another celestial body the ellipse itself does not rotate in any way. Astronomical observations identified systems of double stars, with some of those systems showing an elliptical orbit. All the observations pointed in the direction of those elliptical orbits not rotating. This was strong corroborating evidence that the reference for rotation is the same everywhere in our galaxy. In other words, strong corroborating evidence that rotation is absolute.
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An observer in a noninertial frame of reference observes fictitious forces such as, in the case of a rotating frame, the centrifugal and Coriolis forces. These forces violate Newton's third law, because they're not an interaction between two objects. An inertial frame is defined as one in which Newton's laws hold.