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 → dynamics ↓


Relative speed


Relative motion is a fundamental concept in classical mechanics that describes how the motion of an object is observed from different frames of reference. It involves understanding how the position, velocity, or acceleration of one object relates to another. This relationship is essential for analyzing and predicting the motion of objects in various scenarios in physics.

Understanding the frame of reference

To analyze relative motion, it is important to understand what a frame of reference is. A frame of reference is a perspective or viewpoint from which the position and motion of objects are observed and measured. It includes a coordinate system and a time measurement against which motion can be compared.

For example, suppose you want to analyze the motion of a car moving on a highway. You can have two different frames of reference:

  • Ground frame of reference: The observer is stationary on the ground. The road is the reference point.
  • Reference frame of the car: The observer is moving with the car. The car appears stationary to the observer; other objects, such as trees or other vehicles, appear to be moving.

Relative velocity

Relative velocity is a straightforward concept when considering relative motion. It represents the velocity of one object as viewed from another object. For example, if you are jogging on a treadmill, your velocity relative to the treadmill is zero, even though your velocity relative to someone standing outside the moving treadmill is not zero.

The mathematical relation between the velocities of two objects is given as:

    V AB = V A - V B

Where:

  • V AB is the velocity of object A relative to object B.
  • V A is the velocity of object A in a fixed reference frame.
  • V B is the velocity of object B in a fixed reference frame.

Textual example of relative velocity

Consider two vehicles, car A and car B, moving on a straight road:

Scenario: Car A is moving at 60 km/h, and car B is moving at 40 km/h, both in the same direction. What is the velocity of car A relative to car B?

Use of the formula:

    V AB = V A - V B = 60 km / h - 40 km / h = 20 km / h

Hence, car A moves at a speed of 20 km/h relative to car B.

Graphical example

Car ACar B20 km/h

Relative position

Like relative velocity, relative position refers to how the position of one object is perceived from the frame of another. If you stand at a fixed point, the position of everything else is evaluated based on your location.

The equation for relative position is:

    R AB = R A - R B

Where:

  • R AB is the position of object A relative to object B.
  • R A and R B are the positions of objects A and B in a given reference frame.

Advanced example

Imagine two boats moving in opposite directions on a river. Boat A moves east at a speed of 10 m/s, and boat B moves west at a speed of 15 m/s. The relative velocity of boat A relative to boat B is calculated as follows:

    V AB = V A - V B = 10 m / s - (-15 m / s) = 25 m / s

Therefore, from the point of view of boat B, boat A is moving at a speed of 25 m/s.

Also, let us solve for their relative position after a certain period of time. Suppose both boats start from the same point. After 5 seconds, calculate their relative position:

    R AB = R A - R B
    R a = 10 m/s * 5 sec = 50 m
    RB = -15 m/s * 5 sec = -75 m
    R AB = 50 m - (-75 m) = 125 m

The relative position is 125m.

Graphical representation of acceleration

Just like velocity and position, the concept of relative acceleration is used. If object A has acceleration a A and object B has acceleration a B, then the relative acceleration is:

    a ab = a a - a b
An AB

Conclusion

Relative motion is an essential and interesting topic within classical mechanics that helps us understand how different observers can perceive motion. At its core, it allows us to look at situations from different perspectives and better understand complex systems by breaking them down into interactions between simpler systems. Appreciating the subtleties of relative velocity, position, and acceleration can greatly enhance the ability to understand and predict physical phenomena.

By mastering relative motion, students not only deepen their understanding of physics but also equip themselves with valuable tools for problem-solving in many real-world applications, from engineering and navigation to virtual simulations.


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Relative speed

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