              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  # Rotational Kinematics

SI units & Physics constants

Rotational kinematics investigates lows of motion of objects along circular path without any reference to forces that cause the motion to change Here (all units see here): is initial time on time interval in seconds is final time is original angular position at time in radians is final angular position at time  is angular displacement during time  is original linear velocity vector at time tangent to trajectory is final linear velocity vector at time , tangent to trajectory is total linear acceleration vector, in plane of motion is normal component of total acceleration vector is tangential component of total acceleration vector is radius vector of trajectory, normal to trajectory is length of path during time  is angular velocity vector, normal to plane of motion is angular acceleration vector, normal to plane of motion

## General formulas

Angular displacement Average angular speed on time interval  Instantaneous angular speed at time  Original angular speed at time  Instantaneous angular velocity vector where is unit vector of z-axis shown in the above diagram

Instantaneous angular acceleration vector Linear velocity vector is defined by vector product, where is perpendicual to  Magnitude of linear velocity Magnitude of normal component of total linear acceleration Magnitude of tangential component of total linear acceleration Total linear acceleration vector is defined by vector sum Magnitude of total linear acceleration Angle between linear acceleration and linear velocity vectors Relation between angular acceleration and angular velocity Kinematic equation for rotation ## Uniform rotation   ## Uniformly accelerated rotation   At the rotation is accelerated

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