              home  physics online guide physics help my info terms of use contacts    What is Physics? Mechanics Electricity and Magnetism Electric Field Gauss' Law about below subjects Electric Potential Capacity Direct Current Magnetic Field Magnetic Field Laws Magnetic Interactions Electromagnetic Induction Maxwell's Equations Oscillations and Waves Simple Harmonic Motion Damped Harmonic Motion Driven Harmonic Motion Electric Oscillation Alternating Current Wave Motion Elastic Waves Electromagnetic Waves Optics Light Waves Geometrical Optics Interference Polarization Diffraction Fraunhofer Diffraction Dispersion, Absorption, Diffusion Doppler Effect Thermodynamics Ideal Gas Molecular Statistics Transport Phenomena First Law of Thermodynamics Second and Third Laws of Thermodynamics Imperfect Gas Liquids Solids Quantum Physics Thermal Radiation Quantum Properties of Light Wave Properties of Particles Planetary Model of Atom X-Rays Particle in Potential Well Pauli Exclusion Principle Nuclear Physics Solid State Physics Appendices  # Curvilinear Kinematics

SI units & Physics constants

Curvilinear Kinematics investigates lows of motion of objects in space in two and three directions without any reference to forces that cause the motion to change Here (all units see here): is original time on time interval  is final time is position vector at time  is position vector at time  is displacement vector during time  is length of path during time  is mean velocity vector during time  is instantaneous velocity vector at time , tangent to trajectory is total acceleration vector at time  are unit vectors of axes x, y, z respectively

## General formulas

Displacement vector during time is defined by vector difference Average velocity vector during time  Instantaneous velocity vector Average speed during time  Instantaneous speed Total instantaneous acceleration vector Relation between acceleration and velocity vectors Kinematics equation for motion Relation between curviliner and rectilinear kinematics is defined by vector sum where:

x(t), y(t), z(t) are coordinates of position vector as functions of time t, defined by rectilinear kinematics are unit vectors of axes x, y, z shown in the above diagram

## Components of total acceleration vector Where:

R is radius of curvature of trajectory at time  is centripetal acceleration, normal to trajectory and directed to its center is tangential acceleration, tangent to trajectory and parallel to velocity is total acceleration vector

Magnitude of total acceleration Angle between vectors and  ## Projectile motion Where: is original velocity is original angle is free-fall acceleration directed downward

Kinematic equations for x and y components of position vector:  The x and y components of velocity:   home  |  physics online guide  |  physics help  |  my info  |  terms of use  |  contacts Dr. Nikitin © 2010       