Equations of Motion
Newton's Second Law
In words...
In symbols...
Notice that this is a vector equation. Care should be taken to insure that the vector acceleration occurs in the same direction as the unbalanced force vector.
Equations of Motion for a Single Particle
As in statics, a system of forces acting on a particle can be reduced to a single resultant force acting through the particle's center of mass. Therefore, Netwon's second law takes the form
Or in component form,
This relationship is true for any coordinate system.
| Rectangular cartesian |  |
| Plane, normal and tangential |  |
| Plane, polar |  |
Also as in statics, it is important to draw free-body diagrams so that all forces acting on the particle can be identified.
Equations of Motion for a System of Particles
After applying Newton's second law to each particle in the system and simplifying, one can obtain the following equation.
where
- R is now the resultant of the external system of forces acting on the system of particles
- m is the total mass of the system of particles
- aG is the acceleration of the mass center of the system of particles