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


Kinematics is a branch of classical mechanics that describes the motion of points, bodies, and systems of bodies without considering the forces that cause them to move. In simple terms, it is the study of how objects move. There are often two types of motion we consider: motion on a straight path (linear motion) and motion on a circular path (rotational motion). Kinematics focuses on different aspects such as displacement, velocity, and acceleration.

Basic concepts of dynamics

Dynamics can be understood effectively by breaking it down into some basic concepts and parameters.

Displacement

Displacement is a vector that represents the change in the position of an object. It has both magnitude and direction. Displacement is different from distance, which only measures how much ground an object has traveled, regardless of its starting or ending point.

Example: If a car travels from point A to point B and returns to point A, the total distance traveled is the sum of AB and BA. However, the displacement is zero because the final position is the same as the initial position.

A B A

Velocity

Velocity is a vector quantity that refers to the "rate of change of position of an object." It is an important aspect of dynamics because it not only tells us how fast an object is moving but also in which direction it is moving. The formula for velocity is:

velocity = displacement / time

Example: If a person walks 5 meters east in 5 seconds, then his velocity towards east will be 1 meter per second.

Start 5 minutes V

Acceleration

Acceleration is a vector quantity defined as the rate of change of an object's velocity. It can be positive (speeding up) or negative (slowing down), and is described by the formula:

acceleration = change in velocity / time

Example: If a car increases its velocity from 10 m/s to 20 m/s in 5 seconds, the acceleration will be 2 m/s².

0s / 10m/s 5s / 20m/s

Equations of motion

In dynamics, there are three main equations of motion that relate displacement, velocity, acceleration, and time. These equations assume constant acceleration.

First equation of motion

This equation relates velocity, acceleration, and time:

v = u + at

Where:

  • v = final velocity
  • u = initial velocity
  • a = acceleration
  • t = time

Example: If a car accelerates from rest (0 m/s) at a rate of 3 m/s² for 4 seconds, then the final velocity will be:

v = 0 + (3 * 4) = 12 m/s

Second equation of motion

This equation takes into account the initial velocity, time, and acceleration to calculate displacement:

s = ut + 0.5 * a * t²

Example: For an object with an initial velocity of 2 m/s that accelerates at 2 m/s² for 3 seconds, the displacement is:

s = 2 * 3 + 0.5 * 2 * (3)² = 12 meters

Third equation of motion

This equation relates initial and final velocity, displacement, and acceleration:

v² = u² + 2as

Example: An object with an initial velocity of 5 m/s is accelerated to 15 m/s over a displacement of 50 m. Calculate the acceleration.

15² = 5² + 2 * a * 50
225 = 25 + 100a
200 = 100a
a = 2 m/s²

Graphical representation of motion

Graphs are a valuable tool in studying kinetic motion because they provide a visual representation of the equations we are discussing. Common graphs include:

Displacement-time graph

These graphs show displacement on the y-axis and time on the x-axis. The straight line represents constant velocity, while the curved line represents acceleration.

constant velocity Acceleration

Velocity-time graphs

These graphs show how velocity changes over time. A horizontal line represents constant velocity, while a sloping line represents acceleration, with the slope indicating the acceleration value.

steady Acceleration

Acceleration-time graphs

These graphs measure how acceleration changes over time. A horizontal line represents constant acceleration, which often coincides with the graphs discussed above.

Constant Acceleration

Practical applications of dynamics

Understanding dynamics is important for predicting the motion of objects in various fields such as engineering, robotics, astronomy, and sports.

For example, in sports, analyzing an athlete's motion can help improve performance techniques and reduce the risk of injuries. Engineers designing vehicles such as cars or airplanes use the principles of kinematics to predict how changes in speed and velocity can affect safety and efficiency. In the field of robotics, kinematics aids in programming robots for specific tasks that involve motion.

Conclusion

Kinematics is a fundamental aspect of physics that plays a vital role in understanding the motion of objects. Using simple equations and representations such as graphs, it provides information about displacement, velocity, and acceleration without involving the forces that come into play. With a strong grasp on these concepts, predicting and analyzing motion becomes accessible, aiding many disciplines that rely on these principles.


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