# Newton’ Laws of Motion

Isaac Newton existed between mid-17th century and late 20’s of the 18th century. Although he was not a confirmed student at the Cambridge College, he studies there until he obtained his degree in physics and mathematics. His personal life was not as smooth as we would expect such a philosopher to be. His relationship with his mother was not a very interesting for he had protested his mother from marrying again after his biological father died. His school life was also disturbed by several issues including his mother who wanted him to become a farmer and also the Great Plague of 1665 which forced Cambridge College to close for two years. However, these problems can be assumed to be the normal challenges anyone may or faces today, so he did not give up his passion of studying mathematics and physics. Having been inspired by principles, books, philosophies, and teachings of Kepler, Aristotle, Galileo, Copernicus, and Descartes, he acquired knowledge in the disciplines of mathematics, physics, astrology, and optics.

Isaac Newton’s passion for mathematics and physics and other related studies led to his discovery and drafting of laws and books respectively on the respective disciplines. Amongst some of Newton’s remarkable books include the principles of mathematics (Newton, 1667) while his remarkable theories include the laws of motion and the calculation of the escape velocity in astronomy. As mathematics and physics were his preferred disciplines, he was also interested in philosophy as well as theology.

Besides challenges in the life of Newton, he survived them and emerged as one of the most important scientist of all times for his theories, laws, principles, and philosophies are some of most widely used in the world’s mathematics and physics’ fields. Besides his own discoveries and fathering of ideas, he collaborated with other scientists to further on their ideas or help accomplish scientific projects. For example, he used Descartes’ integration and differentiation methodologies and ideas to come up with Binomial series. In this paper, we will discuss Isaac Newton’s Laws of Motion as well as their use in day-to-day life as contribution in modern science and future discoveries.

Newton’s Laws of Motion

1st Law of Motion

Newton’s first law of motion argues that an object in motion will remain in motion as long as there is no force acting on it. The same way, an object that is moving towards east at a speed ‘n’ will move towards that direction unless a different opposing force changes its course. For the case of stagnant or still objects, they remain in a still state unless a force acts on them hence making them move. In conclusion, the first law of motion states that objects, both moving or still will assume their states as long as possible given that they are free of other forces’ influence or effect (Feynman,1964; Newton, 1667).

2nd Law of Motion

Newton’s second law of motion states that the acceleration of an object depends on applied force relative to the mass of the object. A demonstrative to show this phenomenon would require an object of mass 2m and a corresponding force 2 times m. Through this, it means that any mass of an object will not be moved from its state of rest unless a force larger than its mass is applied. For example, a car stuck in the mud will not move unless pulled or pushed by a force larger than the resistance force of the mud and the partial mass of the car is applied. According to Newton, the velocities and changes on motion of an object can only be determined if only the acceleration of such objects were known (Feynman, 1965; Newton, 1667). It is through acceleration that the change of motion and motion of an object is determined given that specific time of its position and the speed at which it was travelling is known. Mathematical representation of the second law of motion is as follows:

1. F = ma
2. a = F/m
3. m = F/a

The meaning of the first equation is that force is product of mass and acceleration and that it can only be determined if the acceleration and the mass of the object are known.

For example:

An object of mass 3.2 Kg accelerating at the rate of 3m/s will be moved by a force that results as a product of 3.2 Kg and 3m/s2 (3m/s divided by 1m/s) hence giving 9.6N. which can be represented mathematically like;

F = 3.2 Kg x 3m/s2

= 9.6 N

Equation 2 means that for instances where the Force and mass of an object are known, the acceleration of the body can be determined. In an example where an object of 200gms is moved by a force of 4N, acceleration can be determined through;

a = 4N/0.2Kg

= 20m/s2

The case of equation 2 applies for equation 3 in that the knowledge of acceleration and force would lead to the determination of the mass. The above method of calculating acceleration will be used to determine mass. Consider a formula one racing car accelerating at the rate of 35m/s2 using a force of 4,500 N (consider negligence to resistance)

m = 4500/ 35

= 128.57143 Kg

3rd Law of Motion

The third law of motion is for opposing forces within which the direction and speed of different objects is affected by action and reaction of different forces. For an example, consider New and Ton who are pulling the extreme ends of a rope. When New pulls hard, unless Ton readjusts himself he will be moved. Likewise, if Ton lets go of his end of the rope, New will be forced to move to adjust he force he was applying and the release of the other opposing force exerted by Ton (Feynman, 1965, 1965, 1985; Newton, 1667).

Discovery of the laws of Motion

The First Law of Motion was discovered by Galileo and furthered by Descartes in that it was argued that the speed of an object will not change unless an external influencing force was present. The statement by Newton is rather considered obvious but in real sense it is far from obvious considering the times within which Galileo existed and the application of Newton’s theory centuries later. The Greek philosophers said that an object’s state remains to be at rest was an influencing factor to the discovery and prove of the first law of motion. However, Galileo observe the movement of objects and concluded that the speed of an object will only be changed through friction. Galileo argued that if the frictional forces were altered, an object set to motion on the surface of the earth would remain in motion forever. According to Newton, Galileo’s theory was correct only that he did not consider the fact of changing course and maintaining the same speed.

The Second Law of Motion was developed by the consideration of inertia in which every object is believed to possess the ability of resist change of state. The states that an object will assume include that of movement or that of rest. Newton’s development of the second law of motion depended on this idea that any object will not move unless a force greater than its mass is applied. At the same time, he experimented that an object in movement will resist change acceleration unless more force is included. The tendency is that any object in a state of movement will move in one direction until an external force intercepts it. Through this, the formulation of force being a product of mass and acceleration was done from an inertia perspective (Hanc, Tuleja, and Hancova, 2003; Newton, 1667).

The Third Law of Motion is formulated from the principle of action and reaction. It is was argued that objects that are connected or made to move by others through a certain medium applied equally opposing forces as those applying the force. For this reason, forces were considered to be opposing each other in respect to their speed and or direction of movement. Consider the mechanism of the steering wheel of either an automobile or a bicycle, as the controller moves to the steering wheel to direct or redirect the vehicle towards a certain direction, resistance from the mass of the vehicle or bicycle causes the opposing force.

EXTENDED THEORY

Momentum

Momentum is the product of velocity and mass of an object that is causes the speed of movement of an object to change. It is argued that momentum is a conserved quantity meaning that an object stored in a closed confinement in total absence of external forces will maintain a constant momentum. Considering this idea, it is true that the motion of an object will increase relative to its mass and velocity in respect of other forces. The velocity of a free falling object will increase from the initial velocity of 0 m/s to nm/s while the mass of the object will remain the same. However, when falling free, the object will be pulled by the gravitational pull that acts on the mass of the object hence resulting to increasing velocity. Assuming it is free fall on an endless space, the object will attain it maxim momentum and therefore be in a state of constant speed that will not reduce or increase at the circumstances. As much as forces play an active role, maximum momentum will only be achieved in a vacuum where there is no air resistance. The relation between momentum and motion is that momentum is a result of velocity, which is a component of motion and at the same time is resulting effect of velocity and mass (Williamson, 1944).

Friction

Friction is the resulting force that an object faces or exerts on another body if it is made to move on the surface of that other object. For this reason, friction is a resistive force that one moving force may be submitted to by an opposite moving object or by a nonmoving object if they come to conduct. In the case of an object where an object is moving at a constant speed of 12km/h and is brought into conduct with another object at the state of rest or moving at an equivalent speed; resistance of movement will be witnessed while the margin of resistance will be dependent of the objects surface and resulting force from the pressure exerted by one object to the other. Following this, the role of friction in motion can alter speed of a moving object as defined by the first law of motion. The importance of friction’s resistive force is in the mechanism and structuring of breaking systems that depend on it for stooping objects in motion. At the same time, astronomers who have to rely on escape velocities to get through to the strata determine the amount of resistance they have to face from air and modify the structure of their spacecraft (Huygens, 1690).

Conservation of Momentum

Momentum remains constant in the case of closed systems except for the cases where certain characteristics of the enclosed system are not obeyed. Consider a case where as a child you are trapped in a shopping cart and you want to move along or backward along a leveled floor while the wheels of the cart are well lubricated thus there is zero friction between the floor and the wheels. One would expect swinging back and forth to result to a significant change of motion or a displacement. However, considering the second law of motion, the swinging of the body results into a forward movement that should make the cart to move along; but on the other hand, the cart exerts equal and opposite force that cancels the initial forward force. For this reason, it is relatively understandable that a closed system obeys the second law of motion in that velocity and mass will result to a change in force. The third law of motion results to the cancellation of the forces since they are equal and opposite of each other. Conservation of momentum is related to motion in that forces that are supposed to result to a change of movement are equal and opposite of each other and obey the dissertation of the second and the third law of motion (Ogborn & Whitehouse, 2000).

Speed

In kinematics, speed in the rate of change of its position and a scalar quantity. Speed does not have direction in that we cannot talk of negative speed. Whether headed forward of behind, the speed of the object as long as it is in motion remains positive and when coming to a stop, it still remains positive till it settles at zero. In this case, the velocity of an object will define speed of the object as well as the acceleration of the object. Once an object changes its state from rest to movement, it acquired positive rate of change of its position. In relation to acceleration, initial and final velocities will result to the calculation of acceleration given that time within which the change took place is known. As defined by the equation (v1-v2)/t = a, where v1 is the initial speed of the object, v2 is the final speed of the object, t is the time taken for the object to move from v1 to v2, and a is acceleration; it means that if time, force, and the mass of an object is known then the difference of the initial and final rate of change can be determined hence finding speed. Thus;

a = F/m = (v1-v2)/t

(v1 - v2) =Ft/m (Newton, 1667)

Velocity

Velocity is the change of the rate of position of an object which defines speed while at the same time is used to calculate acceleration. The significance of velocity is that it is used together with the mass to calculate momentum of objects. The velocity of the body with respect to the mass of the body is responsible for momentum of the body. However, in the closed systems the velocity of a body that results to a force that can be used to determine acceleration this does not apply in regards to the third law of motion. The reason for this is because of the presence of cancelling forces that act as action and reaction forces. Following this, the velocity of anybody in the context of motion under the three laws of motion by Newton is that it is used to calculate other forces that are responsible for the altering of speed, attaining of maximum speed, resistance by friction, and gravitational pull. The relevance of velocity in accordance to the above elements of motion is that is determines the speed that objects cover from one position to the other while at the same time giving grounds of estimation to the amount of required force to put the objects to rest (Feynman,1985).

Acceleration

Acceleration is the increase or reduction in the change of the rate of change of an objects position. The acceleration of an object is determined by the differences of velocities from the time of beginning to the time of ending. Velocities are not calculated only for those objects at rest and then acquiring some movement but also for those moving at a known speed from one point to the other in respect to time. If time is not known but the initial and final speeds and the resulting acceleration are known, then calculation of time can be achieved following the formula below;

t = (v1-v2)/a

For the case of calculating initial or final velocities, the application of rational inequalities is useful. This is as follows assuming that time t, V1, and acceleration is given;

ta = v1-v2

v2 = - (ta-v1)

v2 = - ta + v1 (Feynman, 1965)

Note: Incase the result of the equation is a negative, it should be known that velocity is not a vector quantity and it is assumed to be positive inspite of the rare occasions of negative results in calculation. In accordance to the force that may be resulting from velocity of a body or any other source, acceleration of any object will obey the second law of motion unless it is in the case of Photons, and black holes, which are almost mass less and possessing very high gravitational pull respectively.

Resistance

Resistance is the opposition of motion for objects that exert frictional force to others or it is exerted to them. In thermodynamics, the laws of motion are not obeyed due to the resistance fluids cause objects travelling through them. Also, the speed of sound and the resistance different objects may offer does not obey the laws of motion. However, for clarification of the resistance offered by various forms of matter is different from that offered by actual independent forces. There is a difference between the resistance offered or caused by friction of grinding objects from that offered by viscous fluids (Huygens, 1690).

Considering resistance under friction, it is the resulting effect of opposition that different, equal or varying forces cause on each other. Opposition is relatively proportional to velocity as it is secondarily affective of acceleration. This means that since frictional forces cause velocity drop and difference of initial and final velocities, it is the secondary affecting issue for acceleration and in momentum of free objects (Newton, 1667).

Gravity

Gravity is the principle in which gravitational pull is calculated as well as the weight of objects. Through gravitational pull, the first and the third laws of motion are obeyed. By considering that the first law assumes that objects would stay in motion unless they face opposing forces. For this reason, gravity is a force that affects the motion of upward projectiles in that it opposes their ascension velocities hence bringing them to a neutral point where shortly they possess zero velocity before they start dropping towards the center of gravity. Considering the center of gravity of objects, one would understand the reason why some objects like an elephant cannot run effectively downhill. Relative to motion, gravity affects the third law of motion in that is one of the opposing forces that cause reaction because of other forces. In relation to resistance, gravity resists the motion of objects moving in the opposite direction while relative to acceleration, it results into a change of velocity through time (Newton, 1667).

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