Newton's Laws

NEWTON'S FIRST LAW

Newton's first law, also known as Newton's Law of Inertia, tells us that if no external force acts on a body, it will remain at rest or move in rectilinear motion at a constant speed.

Motion is relative, meaning that it depends on the observer describing the motion. For example, for a passenger on a bus, the passenger sitting next to the bus is moving, while for someone looking at the bus from the outside, the passenger is moving at the speed of the bus. You need a reference system to refer to the motion.

Newton's first law is used to define the reference systems known as Inertial reference systems. Reference systems are those systems from which a body on which no net force acts is observed to move with constant velocity.

In the study of mechanics on Earth, assuming a fixed observer on Earth is a good approximation of an inertial system.

NEWTON'S SECOND LAW

In the Newton's first law We have seen that it takes a force for a body to change its state of either rest or rectilinear motion. Forces are the result of the action of one body on another.

The Second Law of Motion relates the motions of bodies to forces. The statement of Newton's Second Law tells us that the force applied to a body is proportional to the acceleration of the body and its mass. The formula with which to express this second law is:

F = m a

Both force and acceleration are vector quantities, i.e. they have, in addition to a value, a direction and a sense. Newton's second law must therefore be expressed as:

F = m a

The unity of force in the International System is the Newton and is represented by N. A Newton is the force to be exerted on a body of one kilogram of dough to acquire an acceleration of 1 m/s²that is,

1 N = 1 Kg - 1 m/s²

Newton's second law formula can be applied as long as the mass is constant. Sometimes the mass is not constant, for example in the case of a rocket burning fuel. A generalisation of Newton's second law is to define the magnitude of the quantity of motion.

The amount of movement which is represented by the letter p and is the product of the mass of a body times its velocityi.e:

p = m - v

The quantity of motion is also known as linear momentum. It is a vector quantity and is measured in Kg-m/s . In terms of quantity of motion, Newton's second law is expressed as follows:

F = dp/dt

The Force acting on a body is equal to the time variation of the quantity of motion or linear momentum: From this expression of Newton's second law we can derive the Principle of conservation of the quantity of motion. If the acting forces are zero, i.e. we have this equation:

F=0⇒dp/dt=0⇒p=cte
m=cte⇒v=cte

Conservation of the quantity of motion can also be generalised to a particle system. A particle system is a set of bodies or particles whose motion we want to study.

p=p1+p2+p3+...+p

Although the quantity of motion of the system remains constant, the quantity of motion of each particle can vary. The principle of conservation of the quantity of motion is a fundamental principle that holds without exception and has been confirmed experimentally. The variation of the quantity of motion is known as the impulse.

NEWTON'S THIRD LAW

As discussed in the Newton's Second Law forces are the result of the action of one body on another.

Newton's third law is known as Principle of action and reaction. This law states that if a body A exerts an action on another body B, the latter exerts on A another action of equal and opposite direction.

This is something that we can see on a daily basis on numerous occasions. For example, we can find it in these cases:

• 2 balls collide, after the collision the 2 balls move in opposite directions. This is because the force exerted by the A ball on the B ball is the same and in the opposite direction as the B ball on the A ball.
• When rowing in the water, the oar exerts force on the water, and it is the water with the reaction force that pushes us in the opposite direction.
• As a rocket takes off into space, it is the force of the gases on the ground that causes a force of equal magnitude but opposite direction to lift the rocket into the sky.
• When firing a shotgun, there is a recoil force from the shotgun of equal intensity but in the opposite direction to the bullet.
• As we stand on the ground, the same force that we exert on the ground, the ground is exerting on us.

Even if the action and reaction pairs have the same value and opposite directions, are not cancelled each other, since act on different bodies.