.If any external force doesn’t compel an object to change its way of moving, the object continues to move always in the same way: If the object was at rest, it remains at rest, if the object was moving with a uniform velocity motion along a straight line it continues to move with the same uniform velocity.
Briefly, the first law states: unless there is a force acting on the object, its velocity will not change.
The first law contradicts Aristotle’s thought; Aristotle believed that if an object moves, there must be a force to keep the object moving. This is intuitive but incorrect, in effect in everyday life if we stop making force on the object (for instance a skate-board), it will rapidly slow down and stop, but this is just because there are other forces acting during the movement: frictional forces, air resistance and so on. These parasitic forces offer resistance to the movement, but if we imagine eliminating them (ideal case), after an initial push, one object can continue to move forever. This is the great intuition of Galileo, well formalized by Newton at the end of the 1600’s.
If the velocity in itself doesn’t involve the existence of forces acting on objects, what is the real index that reveal the presence of forces looking at an object while it moves?
The index is the "change in velocity" or acceleration.
This fact is well-stated by the Newton’s second law:
The acceleration experienced by an object at a given instant is directly proportional to the sum of the forces acting on the object at that instant, and inversely proportional to the mass of the object.
We can write that:
.
If we reverse the formula we can write that the total force acting on the object is the product of the mass of the object and the acceleration to which the object is subjected:
.
By analysing this formula we deduce that force is a vector: it gets the same direction of the acceleration vector of the object.
Its unit of measurement, called Newton (N), is equal to
.
The mass of the object is the proportionality constant between acceleration and force, it indicates how much resistance an object offers to a change in its motion. It is responsible for the inertia of the object. Physically speaking, the mass is a property of the object related to the quantity of matter making up the object. It is a physics property of the object.
The first and second law allow us to make a clear distinction between weight and mass, this two words are a little bit confused in the common language, but they have profoundly different meanings.
Mass is a property of the object.
Weight is a force. Which force is it?
Weight is the gravitational force.
On the earth’s surface the gravitational acceleration is:
. (downward direction).
Weight of an object is the product of the mass of the object with the
gravitational acceleration the object undergoes. We indicate this
particular force with a capital 
:
it's the weight of an 
mass object.
Weight is a vector and its direction is the same of the gravitational acceleration: straight down towards the centre of the earth.
When you stay on the scale, you say "my weight is n kilos" but this statement is wrong: you have to say "my mass is n kilos". Weight is different and depends on the particular frame you are. For instance a 60 kg man, has different weight in different situations.
| Place | Gravitational acceleration | Weight |
| On the earth surface | |
 |
| On the moon surface |  |
 |
| In outer space, far away from planets |  |
 |
This law states where forces come from.
It states that:
if an object A exerts a force 
on the object B, the object B reacts with a force 
on the object A that is equal in magnitude but opposite in direction to the
force exerted on B:
.
(See examples 4.10- 4.11 - 4.13 on page 62/63 in the textbook.)
In other words, the third law tells us that forces come from interaction with other objects.
In order to evaluate how an object will move when undergoing a system of forces, we have to isolate the object of interest drawing its free-body diagram (a sketch of all the force vectors applied to the object). This lets us establish the total net force acting on the object. For a better understanding we can do some exercises.
Problem CP1 pag.72 in the textbook.
A constant horizontal force of 20N is exerted by a string attached to a 3Kg block being pulled across a table top. The block also experiences a frictional force of 5N due to contact with the table.
From the second law we have
letting the positive direction be rightward we can write
rightward directed (the total sign is plus).
hence
(rightward direction).
This is a uniform acceleration motion where
(rightward direction)
to compute the velocity we have to use the formula of the uniform acceleration motion:
.
For the uniform acceleration motion we have:
.
Problem CP4 pag.72 in the textbook.
A 75 Kg man is in an elevator that is accelerating downward at the rate of
.
, the man’s true weight isLetting be positive the upward direction
(downward direction).
The total net force acting on the man can be computed with the second law
(downward direction)
The man in the elevator experiences two kind of forces:
1) Its weight (downward)
2) A normal reaction force due to the elevator’s floor. Therefore the system "man in the elevator" can be represented with a square to which we applies two force vectors as follows
The total force on the man is the vector sum of these two forces
to know
we reverse the last formula
and by using the previous results we have
(upward direction)
Because of the third law the force
.
?
- True weight remains the same.
(upward direction).
(upward direction).
.
(A good explanation of the Elevator Problem can be found on page 64 in the textbook).
