              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  # Translational Dynamics

SI units & Physics constants

Translational dynamics investigates translational motion of objects and deals with effects that forces have on motion Here (all units see here):

m is mass of object is velocity vector is linear acceleration vector is linear momentum vector is force vector

## General formulas and definition

Definition of mass: mass, m, of a substance or a body is scalar quantity, which defines its inertial and gravitational properties. The unit of mass is kilogram, 1 kg, defined by etalon of mass as specific platinum-iridium cylinder

Linear momentum is vector fefined by Force is vector fefined by Resultant force or net force of n forces applied to object is defined by vector sum The polygon rule for net force for case n = 3 ## Some forces in Mechanics

Gravitational force where g is free-fall acceleration

Frictional force where: is coefficient of friction

N is normal component of total force acting on object from the surface Spring force where:

k is spring constant

xo is length of unstretched spring

x lengths of spring stretched by force F

## Newton's laws of motion in inertial reference frames

Inertial reference frame is a frame of reference which is at rest or moving at a constant velocity, which obeys the Newton's First Law

Newton's First Law

If then , that is the object is in uniform motion, or at rest

Newton's Second Law:

- for general case - for constant mass Newton's Third Law where: is force on mass m1 applied by mass m2, and is force on mass m2 applied by mass m1, shown in the below diagram ## Law of conservation of linear momentum

Total linear momentum of system of n particles is defined by vector sum where is linear momentum of i-th particle with mass and velocity The law of conservation of linear momentum

If then where is resultant force of all external forces applied to the system of particles

Totally inelastic collision is the collision after which the objects are moving together as one body The velocity after inelastic collision Totally elastic collision is the collision when total machanical energy conserves in the collision

Collision for unidirectional motion: The velocities of objects after collision:  where is coefficient of restitution

For totally elastic collision For totally inelastic collision ## Impulse-Momentum Theorem

Impulse of force where is average force acting on object during time interval given by integral Impulse-Momentum theorem  where and are initial and final linear momentums of the object respectively

Motion of center of mass of system of particles

The position vector of center of mass of n particles: where: and are mass and radius vector of position of i-th particle is total mass of the system of particles

The velocity vector of center of mass The Newton's Second Law for motion of center of mass where is resultant force of all external forces applied to the system of particles

## Propulsion motion of object with variable mass Where:

m is current mass of object is current velocity of object is trust (or reactive force) is velocity of ejected mass with respect to the object

The thrust force where is rate of change of mass m

The equation for motion of object with variable mass Current speed of object with mass m starting from rest with original mass   home  |  physics online guide  |  physics help  |  my info  |  terms of use  |  contacts Dr. Nikitin © 2010       