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 → Speed and collisions ↓


Linear momentum


Linear momentum is a core concept in physics, particularly within the branch of mechanics. It is used in analyzing the motion and interactions of objects, particularly during collisions. Linear momentum is basically defined as the product of an object's mass and its velocity. This quantity provides the mathematical and conceptual basis for understanding how objects move and how they interact with each other.

Understanding linear momentum with examples

To better understand what linear momentum is, let's consider some examples. Imagine a large truck and a small car are traveling on the highway. If both are traveling at the same speed, the truck, which has more mass, will have more momentum than the car. This means that it is more challenging to stop a truck or change its direction of motion than a car.

Trucks (higher mass) Car (low mass)

In the figure above, the blue bar represents a truck, and the red bar represents a car. Their respective momenta can be represented as follows:

momentum_truck = mass_truck * velocity
momentum_car = mass_car * velocity

Since mass_truck > mass_car, it follows that momentum_truck > momentum_car.

Mathematical expression

In more formal terms, if we have a body of mass m moving with a velocity v, then the linear momentum p is given by the following equation:

p = m * v

Where:

  • p is the linear momentum, which is a vector quantity.
  • m is the mass of the object, scalar.
  • v is the velocity of the object, which is a vector quantity.

Conservation of linear momentum

One of the most basic principles associated with linear momentum is conservation of momentum. This principle states that in an isolated system, where no external forces act, the total linear momentum remains constant.

For example, consider two ice skaters who are initially at rest. If they push each other, they begin moving in opposite directions. Despite the change in their individual momentum, the total momentum of the system remains zero as it was initially.

Examples of conservation of momentum

Let us take two different objects A and B. Before collision, let us assume that object A is moving with speed p_Ai and object B is moving with speed p_Bi. After collision, their momenta change to p_Af and p_Bf respectively.

Conservation of momentum tells us:

p_Ai + p_Bi = p_Af + p_Bf

This equation emphasizes that the combined momentum after the collision is the same as it was before the collision.

Exemplary applications

Consider the game of pool. When the cue ball strikes the stationary 8-ball, momentum is transferred from the cue ball to the 8-ball, causing it to accelerate. Let's examine this using a simplified illustration:

cue ball 8 Ball

In this scenario, if the total initial momentum of the system is given as the momentum of the moving cue balls after the collision, then each ball will share this momentum adjusted for direction and mass.

Motion in different dimensions

Linear momentum is a vector quantity, which means it has both magnitude and direction. In many problems, especially problems involving physics that occur in more than one dimension, it is important to break momentum down into its components. Consider a car moving up a hill; its momentum must be calculated in both horizontal and vertical components:

To drive

Impulsive force and momentum

When discussing changes in momentum, the applied forces over time, known as impulse, are important. Impulse J is related to the change in momentum by the formula:

J = Δp = F * Δt

Where:

  • Δp is the change in momentum.
  • F is the applied force.
  • Δt is the time period during which the force is applied.

Practical example: car security

Impulse and momentum principles are important in car design, especially in ensuring the safety of passengers during accidents. Longer periods of impact (soft crumple zones) reduce the force felt by passengers, which shows the practical use of momentum concepts.

Conclusion

Linear momentum is fundamental in understanding and analyzing motion in classical mechanics. Its conservation provides important insights into the behavior of colliding objects and systems where forces are applied. Understanding momentum not only aids in understanding how the physical world operates, but also contributes to many practical applications in everyday life, from vehicle safety design to athletic strategies.


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Linear momentum

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