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Solving applications dealing with non-uniform circular motion involves force analysis. With a uniform circular motion, the only force acting upon an object traveling in a circle is the centripetal force. In a non-uniform circular motion, there are additional forces acting on the object due to a non-zero tangential acceleration.
The last part of the book returns to the design of a clock where the motion of the pendulum is circular, and the string unwinds from the evolute of a parabola. It ends with thirteen propositions regarding bodies in uniform circular motion, without proofs, and states the laws of centrifugal force for uniform circular motion. [23]
'that which moves without being moved') [1] or prime mover (Latin: primum movens) is a concept advanced by Aristotle as a primary cause (or first uncaused cause) [2] or "mover" of all the motion in the universe. [3] As is implicit in the name, the unmoved mover moves other things, but is not itself moved by any prior action.
These results agree with those above for nonuniform circular motion. See also the article on non-uniform circular motion. If this acceleration is multiplied by the particle mass, the leading term is the centripetal force and the negative of the second term related to angular acceleration is sometimes called the Euler force. [22]
This can be seen as violating the axiom of uniform circular motion. Noted critics of the equant include the Persian astronomer Nasir al-Din Tusi who developed the Tusi couple as an alternative explanation, [ 10 ] and Nicolaus Copernicus , whose alternative was a new pair of small epicycles for each deferent.
Aristotle proposed the existence of divine unmoved movers which act as final causes; the celestial spheres mimic the movers, as best they could, by moving with uniform circular motion. [ 13 ] [ 14 ] In his Metaphysics , Aristotle maintained that an individual unmoved mover would be required to insure each individual motion in the heavens.
By using an equant, Ptolemy claimed to keep motion which was uniform and circular, although it departed from the Platonic ideal of uniform circular motion. The resultant system, which eventually came to be widely accepted in the west, seems unwieldy to modern astronomers; each planet required an epicycle revolving on a deferent, offset by an ...
Hence their motions are eternal and perfect, and the perfect motion is the circular one, which, unlike the earthly up-and down-ward locomotions, can last eternally selfsame - an early predecessor to Newton's First Law of Motion. Aristotle theorized that aether did not exist anywhere on Earth, but that it was an element exclusive to the heavens.