Acceleration
Forces and Motion

The development of Newton’s first law

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Galileo’s comments may have influenced Newton’s development of the first law of motion. In the English translation of The Dialogue, Galileo wrote in the margin:

The motion impressed by the projicient is onely in a right line. The project[ile] moveth by the Tangent of the circle of the motion precedent in the point of separation. A grave project[ile], as soon as it is separated from the projicient, beginneth to decline.

Galileo’s comment can be interpreted to mean that a body released from circular motion will follow a tangent to the circle and a heavy body will begin dropping immediately. A diagram suggests that Galileo assumed that the released body would travel at constant speed. While Galileo can be considered to have noted the three essential components of Newton’s first law, (constant speed motion in a straight line and the effect of an external force), he did not state a universal form of a law of inertia. Newton was also influenced by Descartes. He is said to have taken the form of his law from Descartes’ first law of nature:

…each particular part of matter continues always to be in the same state unless collision with others constrains it to change that state. This is to say, if the part has some size, it will never become smaller unless others divide it; if it is round or square, it will never change that figure without others constraining it to do so; if it is stopped in some place, it will never depart from that place unless others chase it away; and if it has once begun to move, it will always continue with an equal force until others stop or retard it.

Newton was both inspired and irritated by Descartes’ writing and, it is argued, his inclusion of the word Principia in the title of his texts was a jibe at Descartes’ use of the term. Newton did not include an explicit numerical measure or symbol for acceleration in his work; the expression of his second law as F=ma first emerged more than half a century after the Principia was published, in a paper by Euler. Similarly, Cavendish, in his paper Weighing the Earth, makes no mention of the concept of acceleration due to gravity and only refers to the quantities of length and time.

References

Acceleration
appears in the relation F=ma a=dv/dt a=-(w^2)x
is used in analyses relating to Terminal Velocity
can be represented by Motion Graphs
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