Kinematics of particles

Part of the Dynamics course offered by the Division of Applied Mechanics, School of Engineering and the Engineering and Technology Portal

LectureEdit

Equations of MotionEdit

Rectilinear Motion
The motion of any particle is most easily described by using the the equations of Rectilinear Motion. Where   represents distance or displacement,   represents velocity and   represents acceleration, it may be remembered from Physics that:

    and    

Curvilinear Motion
The motion of any particle along a curved path is most easily described by using the the equations of Curvilinear Motion. Where   represents the position of a particle in cartesian or polar coordinates and   is the displacement of said particle, the scalar quantity   represents the distance of the displacement and   is the instantaneous velocity of the particle:

 

3D MotionEdit

Motion in three dimensions may be described by the following equations:
Rectangular Coordinates (Cartesian) - (x,y,z)

  
  
  

Cylindrical Coordinates - (r,  , z)
Also see Polar Coordinates (r,  )

  
  
 

Spherical Coordinates - (R,  ,  )

  
 
 

Mass Moment of InertiaEdit

Mass Moment of Inertia is the resistance of an object to attempts to accelerate its rotation about an axis.

 ,   ,            (4)

If the axis of rotation passes through the center of gravity of the rotating object, the calculated   is called the Centroidal Mass Moment of Inertia. (See also the List of moments of inertia on Wikipedia)

Additive Motion & Relative MotionEdit

For a system of two vectors oriented in different directions, the relationsip between the two may be establshed through vector addition. For vectors   and  , the relative motion of   from the frame of reference of   is:

  

The calculation of relative motion is completed similarly for acceleration.

AssignmentsEdit

Activities:

Readings:

Study guide:

  1. Wikipedia article:Cartesian coordinates
  2. Wikipedia article:Polar coordinates
  3. Wikipedia article:Cylindrical coordinates
  4. Wikipedia article:Spherical coordinates
  5. Wikipedia article:Displacement
  6. Wikipedia article:Distance
  7. Wikipedia article:Velocity
  8. Wikipedia article:Speed
  9. Wikipedia article:Acceleration