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# Isaac Newton: Physics and Calculus

December 1, 2015 | | Leave a Comment

Sir Isaac Newton was an English-born mathematician of the Scientific Revolution. Like many other scientists of this time, he built upon the work of his predecessors, especially Galileo. The Italian astronomer used the telescope to make extremely precise observations of planets and moons in the night sky that had never been achieved before. Newton used these observations to derive his three laws of motion and in doing so, calculus. The relationship between calculus and Newtonian physics is sometimes overlooked and to understand it, we must first define what calculus does.

Put simply, calculus is the mathematical study of change. It describes the change in slopes and rates as a series of increments at many points in time. The foundation of calculus is differential calculus. The derivative of a line is the line’s slope, or rate of change, at that moment in time. This is an extremely important concept in understanding the physical laws of motion because we can now understand how position, velocity, and acceleration are related. An object’s velocity is the rate of change of the object’s position at a specific moment of time, while acceleration is the rate of change of the object’s velocity at a specific moment in time. Therefore, velocity is the derivative of position and acceleration is the derivative of velocity.

It was with this new understanding of calculus and the extensive research of Galileo that Newton was able to calculate his three laws of motion. First, the net force of an object with a constant velocity (i.e. no acceleration) is zero. This is also known as the law of inertia and implies that an object at motion will stay in motion and an object at rest will stay at rest unless another force acts upon it. The second law states that force is equal to the mass of the object times the rate of change, or derivative, of its velocity, also known as force equals mass times acceleration. The second law is also an answer to the obvious question raised by the first law. If an object at rest tends to stay at rest until a force acts upon it, what force acts upon an object when it is at rest and released from a height, causing it to fall? The answer is gravity. An object will have a constant acceleration downward due to the force of gravity. This acceleration is constant among all objects regardless of mass, and the only thing that changes with mass if the force of the object. The third law states that every force exerted in one direction will have the same magnitude in the opposite direction, or every action has an equal and opposite reaction. Absent of friction, if one were to push off of a wall, the same amount of force the person applied to the wall would be applied backward on the person and he/she would slide backwards.

Ultimately, Newton’s contributions have been some of the most significant in the entire history of science and mathematics, practically inventing the entire fields of physics and calculus. Isaac Newton’s legacy as one of the greatest scientific minds in the past millennium is certainly justified.

Sources: http://www.physicsclassroom.com/Physics-Tutorial/Newton-s-Laws

http://www-math.mit.edu/~djk/calculus_beginners/