Newton's laws of motion

Isaac Newton (1642-1727) studied and developed Galileo Galilei 's (1564-1642) ideas about motion and stated three laws which now bear his name. He established the subject of dynamics. His laws are a set of statements and definitions that were believed to be true up until the 20th century. This is because what they state can be proven to a high degree of accuracy in normal conditions, however they are not the universal law of motion, and Einstein's general and special relativity is needed to describe motion close to the speed of light and for very massive objects. However for most situations, Newton's laws still hold true and are used by scientists and engineers to predict patterns in moving objects.

(a) First Law:

If a body is at rest it remains at rest or if it is in motion it moves with uniform velocity (i.e. constant speed in a straight line) until it is acted on by a resultant force.

The second part of the law appears to disagree with certain everyday experiences which suggest that a steady effort has to be exerted on a body, e.g. a bicycle, even to keep it moving with constant velocity (let alone to accelerate it), otherwise it comes to rest. The law on the other hand states that a moving body retains its motion naturally and if any change occurs (i.e. if it is accelerated) a force must be responsible. In the situation of a moving body it is not the force that keeps it moving that matters but the forces that are responsible for stopping the motion. In most cases on earth, this is the friction created between the body and the earth's surface. So in frictionless conditions, a body acted on by a force would continue to move at a uniform velocity until another force changed its motion. So to explain the bicycle situation, it is the force of friction acting on the wheels that is slowing the bike down, so a constant force of exertion (pedalling) is required to maintain the velocity.

The law basically defines that a force is needed to accelerate a body from rest or constant motion.

(b) Mass:

When there is friction, matter has a reluctance to move from rest or constant velocity. This property is called inertia. An example is when a vehicle suddenly stops and the passengers lurch forward due to their inertia wanting them to continue at the same speed.

The mass of a body is a measure of its inertia; the larger the mass, the larger the force that is required to accelerate that particular body. The unit of mass is kilogram (kg) and is the mass of a piece of platinum-iridium that is preserved near Sevres Paris.

(c) Second Law:

The rate of change of momentum of a body is proportional to the resultant force and occurs in the direction of the force.

The momentum p of a body of constant mass m moving with velocity u is, by definition, mu. That is, momentum = mass * velocity.

If a force F acts on a body for time t and changes its velocity from u to v, then the change of momentum = mv - mu, therefore the rate of change of momentum = ''m(v-u)/t. Hence the second law, F is proportional to m(v-u)/t. If a is the acceleration of the body then a = (v-u)/t, according to SUVAT equations therefore F is proportional to ma, or F=kma, where k ''is a constant. One newton is defined as the force which gives a mass of 1 kilogram and acceleration of one metre per second per second. So if m= 1kg and a= 1ms^-2 then F= 1N and substituting these vaules in F=kma we obtain k=1. So with these units we get:

F=ma

This expression is the equation that most people associate with when people mention Newton's 2nd law. It enables people to find the acceleration of a body if there is a known mass and a known force. Again however, the equation works when there is little or no friction and energy considerations need to be taken into account when using the equation. The equation agrees with Newton's first law that a force is required to accelerate a body of mass m. If the body is at rest or moving at a constant velocity, there is no a and therefore no F acting on the body using F= ma.

(d) Weight:

The weight W of a body is the force of gravity acting on it towards the centre of the earth. Weight is a force, due to the fact that a body is being accelerated towards the Earth. Mass however is a constant and its amount is not affected by the presence on Earth. I.e. you may weigh different amounts on the earth compared to the moon, due to the different forces of gravitational acceleration, however you would always be the same mass. If g is the acceleration of the body towrds the centre of the earth then we can substitute F = W and a = g in F=ma, giving

W=mg

If g = 9.8ms^-2, a body of mass 1kg has a weight of 9.8N (roughly 10N). The mass m of a body is constant but its weight mg varies with position on the earth's surface since g varies from place to place. Weight can be measured using a calibrated spring balance.

(e) Third Law:

If a body A exerts a force on body B, then body B exerts an equal but opposite force on body A.

The law is stating that forces never occur on their own but always have a counteracting opposing force, as a result of the interaction between two bodies. For example, when you step forward from rest your foot pushes backwards on the earth and the earth exerts an equal and opposite force on you. Two bodies and two forces are involved. For example if you take a step forward your mass is much less than the earth's so the force you apply on the earth is incredibly small, meaning the earth accelerates a very small amount. However the equal and opposite force the earth acts on your accelerates your smaller mass by a greater amount so you move over a much greater distance. The two opposite forces do not both act on the earth or you when you take a step, otherwise there would be no resultant force and acceleration of bodies would be impossible.