# Newton's laws: statements with examples and importance

Newton's laws (or the fundamental principles of mechanics) are three laws of classical physics that relate the forces acting on a body and the motion of that body. These laws were stated by  Sir Isaac Newton  (also based on Galileo's studies).

Newton's laws are sufficient to explain all the movements of classical mechanics, that is, movements that take place at speeds much lower than the speed of light in a vacuum. All of them can be demonstrated through the application of the scientific method.

These three laws are based on a system of inertial references, that is, with real forces with constant speed.

## Newton's first law: the law of inertia

Newton's first law, also known as the law of inertia, states that:

“Any body maintains a state of rest or uniform rectilinear motion as long as no other forces act on it or the sum of the forces acting on it is zero.”

If a moving object does not receive any extra force, it moves in a straight line with a constant speed. If, on the other hand, we exert a lateral force on this same body, it will change direction. In other words, an object will not change its state of motion unless something does.

### Examples

For example, if you push a box on a frictionless surface, it will continue moving indefinitely unless you apply an opposing force.

On the other hand, if a ball is still on the ground, it will stay still unless something makes it move.

On the other hand, the Moon describes a circular path because it constantly experiences a centripetal force in the direction of the Earth due to the force of gravity with which the Earth and the Moon attract each other  (law of universal gravitation). If the Moon or any other celestial body did not have the influence of the gravity of other planets, they would describe a rectilinear path.

## Newton's second law: law of dynamics

Newton's second law is the fundamental law of dynamics: it establishes the relationship between force and acceleration.

“A force acting on a body gives it an acceleration, proportional to the force and inversely proportional to the mass of the body.”

### Momentum Formula

Mass is a measure of the amount of matter in the body. Newton introduces the notion of momentum. This is a vector quantity equal to the product between the mass and the velocity vector.

p = m · v

Where

• m is the mass

• v is the velocity vector

### Force formula

Starting from the momentum we can deduce the most complete way of defining force for a body of constant mass.

F = m a

Where

• F is the force vector (N)

• m is mass (kg)

• a is the acceleration vector (m/s)

If an object that is at rest does not receive any external force, it will remain at rest. If, on the other hand, we apply a net force, the body experiences an acceleration and acquires a uniformly accelerated motion.

## Newton's third law: law of action and reaction

The third law or law of action and reaction tells us the following:

“When one body acts on another body with a force (called action force), the second body also acts on the first body with a force (called reaction force) of the same size and direction, but in the opposite direction. This principle is also known as the principle of action and reaction.”

### Examples

A classic example of this law is the momentum of a space rocket. When gases are ejected rearward from the rocket motor, they exert a forward force on the rocket, causing it to accelerate in the opposite direction.

Newton's third law is also relevant in nuclear energy production. When a uranium nucleus splits into two smaller nuclei (nuclear fission), a large amount of energy is released.

This release of energy is due to the conservation of momentum. The two core fragments move away from each other at high speed as a result of the action-reaction, and this kinetic energy is converted into thermal energy which is then used to generate electricity in a nuclear reactor.

## Examples of applications of Newton's Laws

Newton's laws are fundamental to physics and have a wide range of applications in everyday life and science.

Some examples of areas where these laws are especially relevant include:

• Engineering : Newton's laws are essential for the design and construction of machines, vehicles and structures.
• Astronomy : They are used to predict and understand the movement of planets, stars and other celestial bodies.
• Physics of motion : Newton's laws are the basis of kinematics, which deals with the study of the motion of objects.
• Space engineering: They are crucial for the design and operation of spacecraft and satellites.
• Automotive technology : They are applied to develop safety systems in vehicles, such as airbags and braking systems.
• Biomechanics : They help understand how living beings move and respond to forces applied to them.
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Publication Date: October 30, 2021
Last Revision: September 18, 2023