Newtons Mechanical Synthesis

Newtons Mechanical SynthesisJoseph Sebastian Dee, Danaan Portugal Villena, Tomy Paulino, John Darryl Dy

+ObjectivesBy the end of the report, you should be able to:explain why objects undergo different kinds of motion;state and explain Newtons Three Laws of Motion and the Law of Universal Gravitation;differentiate between inertial and non-inertial reference frames;and characterize physical laws.

+Newtons Three Laws of Motion+Isaac Newton

Sir Isaac Newton PRS MP was an English physicist and mathematician who is widely regarded as one of the most influential scientists of all time and as a key figure in the scientific revolution.

Born: December 25, 1642, Woolsthorpe-by-Colsterworth, United KingdomDied: March 20, 1727, Kensington, United Kingdom+Newtons Laws of MotionFirst Law: Law of InertiaAn object at rest stays at rest and an object in motion stays in motion with the same speed and in the same directionunless acted upon by an unbalanced force

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+Force Is a push or pull upon an object resulting from the object'sinteractionwith another object. Whenever there is aninteractionbetween two objects, there is a force upon each of the objects. When theinteractionceases, the two objects no longer experience the force. Forcesonly exist as a result of an interaction.The state of motion of an object is maintained as long as the object isnotacted upon by an unbalanced force. All objects resist changes in their state of motion - they tend to "keep on doing what they're doing."

+How is this law made possible? Inertia The resistance an object has to change its state of motion.Galileo, a premier scientist in the seventeenth century, developed the concept of inertia. Galileo reasoned that moving objects eventually stop because of a force called friction.

+The tendency of an object to resist changes in its state of motion varies with mass. Mass is that quantity that issolelydependent upon the inertia of an object. The more inertia that an object has, the more mass that it has. A more massive object has a greater tendency to resist changes in its state of motion.Mass The quantity of matter in an object.

+Newtons Laws of MotionSecond Law: Law of AccelerationThe acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.a = Fnet/ m

+Acceleration - Is therateat which thevelocityof a body changes with time.According to Newton, an object will only accelerate if there is anetorunbalanced forceacting upon it. The presence of an unbalanced force will accelerate an object - changing its speed, its direction, or both its speed and direction.

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+Newtons Law of MotionThird Law: Law of Action ReactionFor every action, there is an equal and opposite reaction.

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+In every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first objectequalsthe size of the force on the second object. The direction of the force on the first object isoppositeto the direction of the force on the second object. Forcesalwayscome in pairs - equal and opposite action-reaction force pairs.

+Newtons Universal Law of Gravitation+Newtons Universal Law of GravitationNewton proposed that every object in the universe attracts every other object.

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The constant G, called the gravitational constant, is a proportionality constant necessary to relate the masses, measured in kilograms, to the force, measured in Newtons. In the SI system of units, G has the value 6.67 1011 N m2/kg2+

+Newtons Universal Law of GravitationFurthermore, Newton stated that the force of gravity is always attractive, works instantaneously at a distance, and has an infinite range.It affects anything with mass, regardless of chemical composition or charge. Objects with the same mass fall at the same rate+Weight or Pull of GravityFw = magm = massa = acceleration due to gravityOn earth, acceleration due to gravity is 9.8 m/s2+Consequences of the Law of Gravity Influence of celestial bodies on earths moon causes perturbations in its motion along its path.Predicted reappearance of comets obey the law of gravitation (Halleys Comet ave. period of 75 yrs.) Planets + satellites = spherical, flattened at poles, bulging at the equator --- gravitational force greater in the equatorExplanation for tides Discovery of planets +Inertia and Non-inertia Reference Frames+According to Isaac Newtons Philosophi Naturalis Principia Mathematica (Mathematical Principles of Natural Science) or Principia for short, time and space are both absolute. But what did he mean by both of them being absolute?Time and space are two well known phenomena. Everyone knows and has an idea of these two terms. However, these quantities are usually understood or visualized only through the use of objects of sense perception. +Absolute vs. Relative: Space Absolute space in its own nature, without relation to anything external, remains always similar and immovable. The same goes for space. Newton described space into two different aspects as well: Absolute Space, a quantity which is immovable and unchangeable, and Relative Space, a space measured relative to perceptible bodies.

+In Relation to InertiaInertial frame is the frame of referencethat describes time and space homogenously, isotropically, and in a time-dependent manner. in which Newtons first law of motion applies: an object moves at a constant velocity unless acted on by an external force.It is said that all inertial (reference) frames are in a state of constant, rectilinear motion with respect to one another. They dont accelerate. +On the other hand, a non-inertial frame is a frame of reference that is undergoing acceleration with respect to an inertial frame. This is where the term fictitious forces can be applied. Fictitious forces also called inertial force; is an apparent force that acts on all masses whose motion is described using a non-inertial frame. (ex. Coriolis Effect, Centrifugal Force, Car/Airplane Effect)+

+ConclusionIn Newtonian Mechanics, time and space is absolute. His works and discoveries are truly fruitful; however, his theories on absolute time and space are only valid in inertial frames of references because further studies will show that some of the proposals or laws made by Isaac Newton were actually false. But, even if his theories were wrong, because of him, man is one step closer to understanding the universe and all its mysteries.+Theories of Relativity, Universality and Invariance+In 1905, Albert Einstein determined that the laws of physics are the same for all non-accelerating observers, and that the speed of light in a vacuum was independent of the motion of all observers. This was the theory of special relativity. It introduced a new framework for all of physics and proposed new concepts of space and time.Einstein then spent ten years trying to include acceleration in the theory and published his theory of general relativity in 1915. In it, he determinedthat massive objects cause a distortion in space-time, which is felt as gravity.

+Two objects exert a force of attraction on one another known as "gravity." Even as the center of the Earth is pulling you toward it (keeping you firmly lodged on the ground), your center of mass is pulling back at the Earth, albeit with much less force.Sir Isaac Newton quantified the gravity between two objects when he formulated his three laws of motion. Yet Newton's laws assume that gravity is an innate force of an object that can act over a distance.

+Theory of Special RelativityDetermined that the laws of physics are the same for all non-accelerating observers, and he showed that thespeed of light within a vacuum is the same no matter the speed at which an observer travels. As a result, he found that space and time were interwoven into a single continuum known as space-time. Events that occur at the same time for one observer could occur at different times for another.

+As he worked out the equations for his general theory of relativity, Einstein realized that massive objects caused a distortion in space-time. Imagine setting a large body in the center of a trampoline. The body would press down into the fabric, causing it to dimple. A marble rolled around the edge would spiral inward toward the body, pulled in much the same way that the gravity of a planet pulls at rocks in space.

+General Theory of RelativityGeneral relativitywas Einsteins theory of gravity, published in 1915, which extended special relativity to take into accountnon-inertial frames of reference areas that are accelerating with respect to each other. General relativity takes the form of field equations, describing the curvature of space-time and the distribution of matter throughout space-time. The effects of matter and space-time on each other are what we perceive as gravity.

+The theory of the space-time continuum already existed, but under general relativity Einstein was able to describe gravity as the bending of space-time geometry. Einstein defined a set offield equations, which represented the way that gravity behaved in response to matter in space-time. These field equations could be used to represent the geometry of space-time that was at the heart of the theory of general relativity.

+As Einstein developed his general theory of relativity, he had to refine the accepted notion of the space-time continuum into a more precise mathematical framework. He also introduced another principle,the principle of covariance.This principle states that the laws of physics must take the same form in all coordinate systems.

+Theory of UniversalityThis theory is an attempt to describe the universal phenomena like space, time, matter and energy as an inter-relationship bound by a newly discovered force named as the universal force. The universal force is shown to be the force of gravitation, electricity, magnetism, strong nuclear and weak nuclear forces. I believe any other force, hitherto fore not discovered; also, can be explained in terms of this universal force.

+ Liberal use of wave-particle duality, relativity, quantum concepts is made to achieve a harmonious and comprehensive synthesis of all the existing beliefs in physics into a new theory with some new concepts added here and there. While adding new concepts, enormous care has been taken to ensure that the existing beliefs are not contradicted.+Theory of Invariance Invariance in physics refers to when a certain quantity remains the same under a transformation of things out of which it is build, while covariance refers to when equations take the same form when the objects in the equations are transformed in some way.

+In the context of field theory, one can make these notions precise as follows. Consider a theory of fields. Let a transformationTTIf a functionalF[]of the fields be given (consider the action functional for example). The functional is said to beinvariantunder the transformationTof the fields provided F[T]=F[]+Referenceshttp://www.holisticeducator.com/GodfreyKneller-IsaacNewton-1689.jpghttp://www.math24.net/law-of-universal-gravitation.htmlhttp://www.thestargarden.co.uk/NewtonAndGravity.htmlhttp://www.space.com/17661-theory-general-relativity.htmlhttp://www.dummies.com/how-to/content/einsteins-general-relativity-theory-gravity-as-geo.htmlhttp://physics.stackexchange.com/questions/61347/invariance-covariance-and-symmetry+Referenceshttp://teachertech.rice.edu/Participants/louviere/Newton/newton5.jpghttp://static.ddmcdn.com/gif/newton-law-of-motion-force-ramps.jpghttp://w3.shorecrest.org/~Lisa_Peck/Physics/syllabus/mechanics/newtonlaws/Newton_webpage/2011/lisa2/newton2.gifhttp://mail.colonial.net/~hkaiter/astronomyimagesB/gravity.gifhttp://csep10.phys.utk.edu/astr161/lect/history/gravity.gifhttp://upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Rotating_spheres.PNG/180px-Rotating_spheres.PNG

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