Newton's Laws

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Short Description of Topic

Preface

Newton describes the scientific process well in his book The Principia with this quote

"The constitution of particular things is known by observations and experiments; and when that is done, it is by this rule that we judge universally of the nature of such things in general."

Definitions

Density

"Quantity of Matter is the measure of the same, arising from its density and bulk conjunctly" (Newton). Newton proved that mass of an object is proportional to its weight through experiments with pendulums. With this in mind, Newton defined mass to be the density of matter in a given space. Later it has been shown to be the number of concentric lines of force that are present in a unit of volume. The density of an object can be shown with the equation: Density=Mass/Volume. The mass of an object refers to the product of the density of an object in a given volume. Thus, porous bodies such as sponges are lighter in mass when the occupy the same volume as more rigid bodies such as wood.

Motion

"The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjunctly" (Newton). Newton defines motion to be the absolute translation of all the matter in an object. The motion of the whole body is the sum of the motion of all of its parts. Thus, a body with mass M and velocity V the motion is equivalent to MV. A body double in mass but with equal velocity has absolute motion of 2MV. This is the principle of momentum. The motion of the whole.

Inertia

"Vis insita, or innate force of matter, is a power of resisting by which everybody, as much as it lies, endeavors to preserve its present stat, whether it be of rest or of moving uniformly forward in a straight line" (Newton). This is the basis of the first law of motion that we will be exploring soon. Inertia is the amount of resistance that a body has to a change in velocity and this is quantified by its mass. An object in motion will maintain its rectilinear (straight) motion unless a force changes its motion in a different direction. When this is done, each component of the motion of the object will be added/subtracted separately, which is why it is useful to understand vector notations.

Forces

A force is an action that is exerted on a body that makes it change its state, either of rest of of uniform rectilinear motion. The force only consists in its action. Once the action is completed, it no longer remains in the body that is was impressed upon. This is because a body maintains every new state that it acquires. This can be easily seen by observing the momentum principle: P(f)=P(i)+FnetΔt. The momentum of an object, which we earlier described to be the sum of the motion of its parts and thus its overall motion, is affected by an added force. Some forces work over a greater length of time, such as the continuously changing gravitational force that our sun exerts on the earth and the same that the earth exerts on its moon. The motion of an object is arithmetically affected by added forces. In cases where non-constant forces act over a long time interval, it is useful to use programs such as VPython that can model this quickly.

Centripetal Force

"A centripetal force is that by which bodies are drawn or impelled, or any way tend towards a point as to a center" (Newton). A centripetal force changes the straight motion of an object and makes it move in curvilinear orbits. For example, when throwing a stone in the air, if one wishes to maximize the distance it travels then they can do two things. One, throw it on a planet with less gravitational force for its quantity of matter. Or, throw it with a greater velocity, thus giving it more time for the constant centripetal force of gravity to chip away at its motion and bring it to the ground. Both of these methods will cause the stone to deviate less from its rectilinear course and thus the body will travel farther.

Absolute Quantity

Newton described the absolute quantity of centripetal force as the "center of force " itself. Such as the earth is the center of the gravitational force. The more massive that the earth is, the greater the centripetal force(gravity) it will exert on matter.

Accelerative Quantity

This quantity is what Newton described to be "the place of body". Such as the fact that the gravitational force is much stronger in valleys than on the tops of high mountains. The more distant from the center of force that an object is, the less centripetal force towards the center that it will experience.

Motive Quantity

"The body itself". Newton described the motive quantity of a force to be measured by a change in the quantity of motion, thus the change in momentum of an object. The force that causes this change in motion can be split into a component that is parallel to the motion and one that is perpendicular. These affect the motion of the body individually.

Relative vs. Absolute Motion

Newton's descriptions of relative and absolute motion provided the basis for Einstein to further develop the principles of relativity.

External links

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References

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