In this video we will talk about Newton's three laws of dynamics.
What is dynamics? It is a part of mechanics that studies the cause of the movement of bodies,
that is, it tries to investigate why bodies move,
and how to characterize this movement. Mechanics in turn is a branch of physics, the same science
that allows us to explain different phenomena that we can observe in nature or the movement
of stars and planets. The conceptual foundations of dynamics were first exposed
by the English physicist Isaac Newton in his work “Philosophiae Naturalis Principia Mathematica”.
But who was Isaac Newton? Isaac Newton was born on January 4th 1643 in Woolsthorpe-by-Colsterworth,
England. As a boy, his parents, farmers, tried to make him work on the family farm,
but without too much success: just think that, instead of looking after the cattle,
the young Isaac preferred to retire to read and study; distracted from his studies, one day he did
not notice that a pig trespassed on a neighbor's farm, and his mother, due to this negligence,
was forced to pay a fine. Thanks to his brother William, the family’s egghead, who had understood
that Isaac was not cut out for peasant life, Isaac in 1661 began attending Trinity College.
During those years, he began to develop the theory of gravitation (it is said that the
idea of ​​the force of gravity came to his mind starting from the observation of the
famous apple's fall). He died in Kengsinton, London, on March 31, 1727, at the age of 84.
Now let's go back to the three principles of dynamics,
starting with the First law of dynamics. Also called the principle of inertia, it states that
"A body not subject to forces or subject to forces whose resultant is zero,
remains in its state of rest or continues to move in a uniform rectilinear motion."
What is inertia? It is essentially the ability of a body to remain in its state of motion or at rest
(that is still), as long as a force is not applied to it, that is something that changes its state of
motion: in practice, if an object it is already in motion, it will continue to move always in
the same direction and at the same speed (that is without accelerating or slowing down) according to
a condition known as uniform rectilinear motion; if it is still it will continue to remain still.
The resultant of forces is the set of all the forces acting on a body.
This principle had already been formulated by Galileo Galilei who had intuited that if you
give movement to a body it tends to remain in motion indefinitely except in the case where a
force intervenes to change its state and brings it back to rest. Let's see some practical examples.
1) When standing on the bus: as long as the bus travels in a uniform straight motion,
our body does not feel anything; when the bus starts or brakes, or is subject to acceleration,
our body, undergoing a jolt, tends to go forward or backward or tends to remain in a state of rest
or in that of motion, and you risk falling to the ground .
2) An ice skater: Those of you who skate or play ice hockey know that if you rush forward
at full speed, you go straight. But what happens when you unfortunately collide with someone?
Your state of motion changes, because an external force (the person you collide with)
intervenes and makes you fall to the ground. If, absurdly, only you were on your skating
rink (so there are no external forces), and if the rink were so big that it was infinite,
you could go straight for hours, and your state of motion would not change.
3) Free astronaut in empty space: if the astronaut acquires an impulse and a certain speed,
he will continue to travel indefinitely if no force intervenes, thus risking getting lost
in space and therefore dying. But this does not happen, because a force holds them close to the
vehicle or space station: this force is produced by the little rockets of the astronauts’ backpack,
which they have to wear when they do spacewalks, or more correctly, extravehicular activities.
The jets that come out of these small rockets are adjustable through joysticks
like those of video games: by acting on these joysticks, the astronauts are able to control
and correct the route in case they inadvertently strayed too far from the station or spacecraft.
4) The spaceship Enterprise in space flight:
if the starship stopped its engines in an area of ​​space sufficiently far from a planet or a star,
or if it had an infinite amount of fuel and was traveling endlessly at a constant speed, it would
move indefinitely with uniform rectilinear motion; if the Enterprise decided instead to
stop at a precise point in interplanetary space, always sufficiently far from a star or a planet
to avoid falling on it, it would remain at rest, or in a state of stasis, indefinitely.
5) Imagine that you are in your car with your parents, and that your dad is driving it while
maintaining a constant speed, that is, without accelerating or slowing down: you are in a
situation of uniform rectilinear motion. Suddenly, to avoid hitting a distracted pedestrian crossing
the street, your dad brakes... what happens? Your state of motion, from a uniform straight line,
changes, because the car stops instantly, due to the force exerted by the brakes on the wheels.
However, you haven’t fastened the seat belts, and you are bumping into the
front seat or the windshield: this happens because, not having fastened the seat belts,
you lack their external force necessary to stop your uniform straight motion.
6) A distracted truck driver talking on the phone while driving: he doesn't notice the
car in front of him! And then it collides badly with the car. The truck is stopped by the impact,
so its state of motion changes, passing from a uniform rectilinear motion situation to
a state of rest ... but the bar placed on the truck roof does not receive any force,
because it has not been well secured to the the roof of the truck, so it continues to
move in a uniform straight line as if nothing had happened and is thrown away in front of the truck.
7) Marbles or balls rolled on a smooth floor: those of you who play with marbles will
surely have noticed that, by rolling them on a smooth floor, they continue forward,
without changing direction: the marbles move with uniform rectilinear motion, therefore always at
the same speed. But if your cat is present in the house, playing with the marbles, it will impress
an external force on them, which will make them deviate from their straight trajectory.
Let's now pass to the second principle of dynamics: also called Newton's second law,
it links the force to the state of motion and in particular states that "The sum of all the
forces acting on a body is equal to the product between mass tand body acceleration: F = ma. "
What does it mean? That the force F and the acceleration a are therefore
two directly proportional quantities, where "directly proportional" means that if you want
to increase the force, the acceleration will increase; if instead you decrease the force,
the acceleration decreases. By dividing the force by the acceleration, the inertial mass
m of a body is obtained, which represents the resistance that a body opposes to the
variation of its state of motion: the greater the mass, the greater the resistance of the body
to vary its state of motion, and the greater the force needed. The smaller the mass,
the smaller the resistance of the body to vary its state of motion, and the smaller the force needed.
Let us also look at some examples for the second principle.
1) Shopping cart: if we apply a force F to push a shopping cart, it will accelerate a. If
the mass of the trolley increases and the same force is always applied, then the acceleration
of the trolley will certainly be lower: this is because, as we fill the shopping trolley,
its mass will increase, so it will be increasingly difficult to move it. If, on the other hand,
we double the force, the acceleration undergone by the trolley will also double.
2) The Enterprise, hit by a meteorite,
lands on a planet: the force of the impact of the meteorite, while not seriously damaging it,
makes it move by one kilometer, that is, it gives the spaceship a change in its speed,
i.e. a acceleration, and also changes the direction in which its movement occurs.
3) Weight lifting: by increasing the number of weights, that is the mass on the barbell,
the athlete must use a gradually greater force to be able to lift the barbell,
making more and more effort and imparting an ever lower acceleration to the barbell.
Finally, let's talk about the Third Principle of Dynamics. Also known as the principle of
action and reaction, it states that "For every action there is an equal and opposite reaction."
That is, if a body A exerts a force F on a body B, the latter reacts by exerting a force F on the
body A. The two forces will be equal but opposite. The main conclusion of this principle is that
forces can never be considered as isolated, but always act in pairs: the interaction between two
bodies is therefore always mutual. Let us also look at some examples for the third principle.
1) Imagine being on a frozen lake, for simplicity. If you take your backpack and throw it,
you too begin to move, from the opposite side to that of the backpack.
2) The third principle of dynamics is the one on which jet propulsion is based,
which allows aircraft to function. The turbine acts by exerting a force on the exhaust gases,
which are then expelled at great speed. In turn, the gases exert a force on the turbine
(and therefore on the plane to which it is connected).
The second force, that is, that exerted by the gases, is the same and opposite to the first.
3) The tennis racket: if you could examine closely and in slow motion what happens during a tennis
match when the ball (body A) hits the racket (body B) at great speed, we would notice that the racket
is deformed by the ball. This means that ball A exerted a force FA on the racquet, called action
force. At the same time, however, it can be seen that the ball is also deformed by the racket.
This means that the racket B has responded to the solicitation and has in turn exerted a force FB,
called reaction. The reaction has the characteristic of having
the same intensity and direction as the acting force but in the opposite direction.
4) The bicycle: why is it impossible to balance on a stationary bicycle?
Assuming you are sitting on a stationary bicycle,
you realize at some point that the bicycle is tilting (for example) to
the left. The natural tendency is to lean to the right, to counterbalance the inclination
with the weight of the body. But by moving your upper body to the right, according to
Newton's third law, you are actually pushing the bicycle to lean more and more to the left.
5) The helicopter: the helicopter has a main rotor with a vertical axis above the cockpit,
and one with a horizontal axis in the tail. The main rotor has the task of generating the support
thrust; it causes a speed variation in the cylindrical column of air above it,
pushing it downwards. The air thus produces an upward thrust that acts on the rotor,
and therefore on the helicopter and allows it to get up.
6) Locomotion: all locomotion systems are based on the Third Principle of Dynamics.
For example, when we walk we push the ground back and the ground in turn pushes us forward with
an equal and opposite force. This generates thrust on one side to advance on the other.
7) A rowing-boat: by moving the oars forward, we produce a certain force on them, pushing the water
backwards; however, the water produces an equal and opposite force, which pushes the boat forward.
8) The Enterprise lands on an oceanic planet:
its weight is balanced by an equal and opposite force exerted by the ocean.