Force
In physics, force is a push or a pull that changes or tends to change the state of rest or uniform motion of an object or changes the direction or shape of an object. Force causes objects to accelerate, add to the object's overall pressure, change direction, or change shape. Force is measured in Newtons. (N).
A force is always a push, pull, or a twist, and it affects objects by pushing them up, pulling them down, pushing them to a side, or by changing their motion or shape in some other way.
Newton's Second Law
According to Newton's Second Law of Motion, the formula for finding force is:
where is the force,
is the mass of an object,
and is the acceleration of the object.
This formula says that when there is a force on an object then it will move faster and faster. If the force is weak and the object is heavy, then it will take a long time to increase the speed very much, but if the force is strong and the object is light, then it will move a lot faster very quickly.
Weight
Gravity is an acceleration. Everything that has a mass is being pulled toward the Earth because of that acceleration. This pull is a force called weight.
One can take the equation above and change to the standard gravity g, then a formula about the gravity on earth can be found:
where is the weight of an object,
is the mass of an object,
and is the acceleration due to gravity at sea level. It is about .
This formula says that when you know the mass of an object, then you can calculate how much force there is on the object because of gravity. You must be on earth to use this formula. If you are on the moon or another planet, then you can use the formula but g will be different.
Force is a vector, so it can be stronger or weaker and it can also point in different directions. Gravity always points down into the ground (if you are not in space).
Gravitational force
Another equation that says something about gravity is:
is force; is the gravitational constant, which is used to show how gravity accelerates an object; is the mass of one object; is the mass of the second object; and is the distance between the objects.
This equation is used to calculate how the earth moves around the sun and how the moon moves around the earth. It is also used to calculate how other planets, stars and objects in space move around.
The equation says that if two objects are very heavy then there is a strong force between them because of gravity. If they are very far apart then the force is weaker.
Images

Aristotle famously described a force as anything that causes an object to undergo "unnatural motion"

Galileo Galilei was the first to point out the inherent contradictions contained in Aristotle's description of forces.

Images of a freely falling basketball taken with a stroboscope at 20 flashes per second. The distance units on the right are multiples of about 12 millimetres. The basketball starts at rest. At the time of the first flash (distance zero) it is released, after which the number of units fallen is equal to the square of the number of flashes.

Relationship between force (F), torque (τ), and momentum vectors (p and L) in a rotating system.
gd:Neart