# Laws of Mechanics

Last Updated: April 25, 2024

## What are Laws of Mechanics?

The laws of mechanics are fundamental principles that describe the behavior of physical systems under the influence of forces. These laws form the foundation of classical mechanics, which is the branch of physics that deals with the motion of objects and the forces that affect them. The core laws of mechanics are encapsulated in Newton’s three laws of motion and the law of universal gravitation.

## The Origin and Foundation of Mechanics

The foundation of mechanics as a science can be traced back to ancient Greece, where philosophers like Aristotle began to systematically explore physical phenomena. Aristotle’s work laid the groundwork for the study of dynamics, particularly with his concept of natural motion and violent motion, although his approach was more qualitative than quantitative.

The real transformation in mechanics, however, came during the Renaissance with the advent of the Scientific Revolution. A pivotal figure in this period was Galileo Galilei, whose experiments and observations challenged Aristotelian physics and laid the foundation for modern dynamics. Galileo’s studies on the motion of objects, characterized by careful measurement and mathematical description, introduced a new level of precision in understanding how objects move.

Johannes Kepler also contributed significantly with his laws of planetary motion, which described the orbits of planets around the sun. Kepler’s laws were empirical in nature, based on meticulous astronomical observations. These laws not only challenged the geocentric models of the cosmos but also provided crucial data for later theories of motion.

The culmination of these developments came with Sir Isaac Newton in the 17th century, who synthesized the works of his predecessors into a comprehensive theory. Newton formulated the three fundamental laws of motion and the law of universal gravitation, which not only explained earthly motion but also celestial phenomena, establishing the modern science of mechanics. Newton’s work, “Philosophiæ Naturalis Principia Mathematica” (Mathematical Principles of Natural Philosophy), published in 1687, is considered one of the most important works in the history of science.

Newton’s laws of motion and universal gravitation provided a unified description of motion, offering a set of principles that could apply to both terrestrial and celestial bodies. These laws are foundational for classical mechanics, providing the framework that engineers and scientists use to predict the behavior of physical systems under various forces. The principles established in classical mechanics have been expanded upon and refined but remain central to the physical sciences, illustrating the profound impact of these early scientific explorations on our understanding of the natural world.

## Fundamental Concepts of Mechanics

1. Force: A force is any interaction that, when unopposed, changes the motion of an object. Force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a push or a pull.
2. Mass: Mass is a property of a physical body and a measure of its resistance to acceleration when a net force is applied. It also determines the strength of its mutual gravitational attraction to other bodies.
3. Motion: Motion is the change in position of an object over time. Mechanics studies the motion of objects: how they move, what governs their motion, and the effects of forces on their motion.
4. Energy: In mechanics, energy is the property of an object that enables it to do work. There are various forms of energy – kinetic energy (energy of motion), potential energy (stored energy due to position), thermal energy, etc. The law of conservation of energy, which states that energy cannot be created or destroyed but only transformed from one form to another, is central to the mechanics of moving bodies.
5. Momentum: Momentum is the quantity of motion of a moving body, measured as a product of its mass and velocity. Like energy, momentum is conserved in closed systems, making this principle a cornerstone of mechanics.
6. Equilibrium: A body is said to be in equilibrium when the forces acting upon it are balanced, resulting in no net force and, consequently, no change in the state of motion of the body. This concept is crucial in statics, a sub-branch of mechanics that studies bodies at rest or moving at a constant velocity.
7. Torque: Also known as the moment of force, torque refers to the rotational effect of a force applied to a rotational system at a distance from the axis of rotation. Torque is pivotal in the study of rotational dynamics, another aspect of mechanics.
8. Dynamics and Statics: Dynamics is the branch of mechanics concerned with the motion of bodies under the action of forces. Statics is the branch that deals with the analysis of loads (force, torque/moment) on physical systems in static equilibrium, i.e., in a state where the relative positions of subsystems do not vary over time.

## Different Laws of Mechanics

1. Newton’s First Law of Motion (Law of Inertia)
2. Newton’s Second Law of Motion (Law of Acceleration)
3. Newton’s Third Law of Motion (Action and Reaction)
4. Law of Universal Gravitation
5. Conservation of Energy
6. Conservation of Momentum
7. Hooke’s Law
8. Bernoulli’s Principle
9. Pascal’s Law
10. Archimedes’ Principle
11. Kepler’s Laws of Planetary Motion
12. Doppler Effect
1. Newton’s First Law of Motion (Law of Inertia): This law states that an object at rest will remain at rest, and an object in motion will continue to move at a constant velocity, unless acted upon by a net external force. It describes the behavior of objects when no forces are present or when forces are balanced, establishing the concept of inertia—the resistance of any physical object to any change in its velocity.
2. Newton’s Second Law of Motion (Law of Acceleration): This law can be expressed with the formula F=ma, where F is the net force applied to the object, m is its mass, and a is its acceleration. It states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This relationship shows how the amount of force affects how quickly an object changes its speed or direction.
3. Newton’s Third Law of Motion (Action and Reaction): This law states that for every action, there is an equal and opposite reaction. This means that whenever one object exerts a force on a second object, the second object exerts a force of equal magnitude and opposite direction on the first object. This law explains the nature of forces between two interacting bodies and is fundamental in analyzing how forces work in pairs.
4. Law of Universal Gravitation: Newton’s law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This law is pivotal in celestial mechanics and explains how and why objects in space (such as planets, stars, and galaxies) exert gravitational pull on each other.
5. Conservation of Energy: This principle states that the total energy in an isolated system remains constant over time. It can be transformed from one form to another (such as potential energy to kinetic energy) but cannot be created or destroyed. This fundamental law of physics underpins virtually every scientific discipline and is essential in studying systems from mechanical to thermal to chemical.
6. Conservation of Momentum: The law of conservation of momentum states that the total momentum of a closed system (i.e., a system with no external forces) remains constant. This means that the total vector sum of the momenta of all objects within the system will not change unless external forces are applied. It is particularly useful in the analysis of collision and explosion scenarios.
7. Hooke’s Law: Hooke’s Law states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance. Mathematically, it is often expressed as F=−kx, where x is the displacement of the spring from its equilibrium position, F is the force applied to the spring, and k is a constant characteristic of the spring known as the spring constant. This law is foundational in the study of elastic materials and simple harmonic motion.
8. Bernoulli’s Principle: Bernoulli’s Principle states that for an inviscid flow, an increase in the speed of the fluid results in a decrease in pressure or a decrease in the fluid’s potential energy. It is a principle within fluid dynamics that helps explain how aircraft wings generate lift, among other applications.
9. Pascal’s Law: Pascal’s Law states that a change in pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and to the walls of its container. This principle underlies the operation of hydraulic systems, including car brakes and hydraulic presses.
10. Archimedes’ Principle: This principle states that the buoyant force on a submerged object is equal to the weight of the fluid that the object displaces. Archimedes’ Principle is key in determining the buoyancy of objects and is crucial in the design of ships and other floating structures.
11. Kepler’s Laws of Planetary Motion:
• First Law (The Law of Orbits): Each planet moves in an elliptical orbit with the Sun at one of the foci.
• Second Law (The Law of Areas): A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
• Third Law (The Law of Periods): The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. These laws describe the motion of planets and other celestial objects, which were revolutionary in moving away from circular orbits and perfect spheres as assumed by earlier theories.
12. Doppler Effect: This phenomenon refers to the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It applies to all types of waves, including sound, light, and radio waves. In sound, it is observed as a higher pitch when the source approaches and a lower pitch when it recedes; in light, this effect can shift the visible colors in the spectrum towards red or blue.

## What is the fundamental law of mechanics?

The fundamental laws of mechanics are Newton’s three laws of motion, which establish the relationships between the forces acting on a body and the motion of that body.

## Which is the golden rule of mechanics?

The golden rule of mechanics is often considered to be the principle of conservation of energy, stating that energy cannot be created or destroyed, only transformed from one form to another.

## What is the first rule of mechanics?

The first rule of mechanics, Newton’s First Law of Motion (Law of Inertia), states that an object at rest stays at rest and an object in motion stays in motion unless acted upon by an external force.

## Is mechanics a math or physics?

Mechanics is a branch of physics that deals with the motion of bodies under the influence of forces. However, it heavily utilizes mathematics to model and analyze physical systems.

## What is the theory of mechanics?

The theory of mechanics refers to the framework and principles that describe the behavior of physical systems under forces and displacements, including statics, dynamics, and fluid mechanics.

## Who is the father of mechanics?

Isaac Newton is often regarded as the father of classical mechanics, due to his formulation of the three laws of motion and the law of universal gravitation.

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