Equation of motion for a particle: Newton’s 2nd law
Newton’s 2nd law: The resultant of all the forces acting on a particle is proportional to the acceleration of the particle.
Newton’s 3rd law: Each action has a reaction equal in magnitude, but opposite in direction
Equations of motion in a rectangular coordinate system: In a rectangular coordinate system the equations of motion can be
represented by three scalar equations:
Example 1:
Example 2:
Equations of motion in normal and tangential (natural) coordinate systems: In a natural coordinate system the equations of
motion can be represented by three scalar equations:
Example 3:
Equations of motion in Cylindrical coordinate systems: In a cylindrical coordinate system the equations of motion can be
represented by three scalar equations:
Example 4:
Free-Body diagram: A diagram showing the particle under consideration and all the forces acting on the particle. Each force in this
diagram must be labeled.
Gravity: The force of gravity is equal to the mass times the acceleration of gravity and is applied at the center of gravity (CG) of the
body.
String or cable: A mechanical device that can only transmit a tensile force along itself.
Linear spring: A mechanical device which exerts a force proportional to its extension along its line of action.
Example 5:
Frictionless and massless pulleys: For a frictionless and massless pulley, the tension in the cable is the same on both sides of the
pulley.
Example 6:
 Mehrdad Negahban and the University of Nebraska, 1996-2002.
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Department of Engineering Mechanics, University of Nebraska, Lincoln, NE 68588-0526