Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Classical mechanics ↓


Newton's Laws of Motion


Newton's laws of motion are three physical laws that form the basis for classical mechanics. These laws describe the relationship between the motion of an object and the forces acting upon it. They were first formulated by Sir Isaac Newton in his work "Philosophiae Naturalis Principia Mathematica," published in 1687. These laws have given us a fundamental understanding of how objects move and react to forces in the universe, which is the basis for much of modern physics and engineering.

First law: Law of inertia

The first law of motion is often stated as follows:

An object at rest remains at rest and an object in motion continues to move with the same speed and in the same direction unless an unbalanced force is applied on it.

This principle is known as the law of inertia. Inertia is the tendency of an object to resist a change in its velocity. In other words, if an object is at rest, it will remain at rest unless a force makes it move. Conversely, if an object is moving, it will continue to move in a straight line at a constant speed unless a force acts on it.

To understand this concept, imagine a hockey puck sliding on the ice. Once the puck is set in motion, it will continue to slide in a straight line and at a constant speed unless acted upon by another force such as friction, a player's stick, or the walls of the rink.

initial situation constant speed

In this diagram, notice how the blue circle (representing the hockey puck) is set in motion along a line. It will continue moving unless an external force (such as friction with the ice, a player's stick, or hitting a boundary) intervenes.

Example of the law of inertia

Consider riding a bicycle. When you pedal, you apply force to the bicycle, which makes the bicycle move forward. If you stop pedaling, the friction between the tires and the ground, as well as wind resistance, will eventually slow the bicycle down and stop it until you start pedaling again.

Second law: Law of acceleration

The second law of motion establishes the relationship between force, mass, and acceleration and can be expressed by the following equation:

F = m * a

Where:

  • F is the net force applied to an object, measured in newtons (N).
  • m is the mass of the object, measured in kilograms (kg).
  • a is the acceleration of the object, measured in meters per second squared (m/s²).

This law states that the acceleration of an object is proportional to the net force applied to it and inversely proportional to its mass. In other words, the greater the force, the greater the acceleration, and the greater the mass, the lesser the acceleration for the same amount of force.

Applied force Mass = 5 kg Acceleration = 2 m/s²

In this diagram, a force is applied to a rectangular block of mass 5 kg. The resulting acceleration of the block is shown by the arrow pointing to the right (red line).

The second law can be used to calculate the force needed to accelerate an object. For example, the force needed to accelerate a car of mass 1,000 kg at a rate of 3 m/s² is:

F = m * a = 1,000 kg * 3 m/s² = 3,000 N

Example of the law of acceleration

Imagine you are pushing two identical shopping carts at the grocery store with the same force, but one cart is empty while the other is full of groceries. The empty cart, with less mass, will gain more speed than the full cart for the same amount of force you apply.

Third law: Action and reaction

The third law of motion states that:

Every action has an equal and opposite reaction.

This law highlights the fact that forces always come in pairs. Whenever an object exerts a force on another object, the second object exerts an equal and opposite force on the first object. This interaction means that the forces are mutual and simultaneous.

Action Force reaction force

In this diagram, the green circle (object A) exerts a force on the blue circle (object B), and simultaneously, object B exerts an equal and opposite force on object A.

Example of action and reaction rule

Consider standing on a skateboard and pushing against a wall. As you push backward against the wall, the wall also pushes you forward with an equal force. The result is that you roll backward on the skateboard as the force is applied to the wall. The forces between you and the wall are equal in magnitude and opposite in direction.

Conclusions and applications

Newton's laws of motion play a vital role in understanding and describing the motion of objects. They allow us to analyze a variety of situations, predict outcomes, and design a wide range of mechanical systems. From engineering feats like bridges and vehicles to simple everyday activities like skating or playing sports, understanding these laws provides a deeper insight into how the physical world operates.

The first law, the law of inertia, explains why objects will not change their motion unless affected by a force. The second law provides a method for quantitatively calculating how forces affect the motion of objects. The third law demonstrates the natural balance and interaction of forces in our world, evident in everything from a rocket launch to the gentle nudging of a book across a desk.

Knowing these laws allows us to delve deeper into more complex physics and solve real-world problems with greater precision, demonstrating the essential legacy left by Sir Isaac Newton in establishing the foundations of classical mechanics.


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Newton's Laws of Motion

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