Part of the Dynamics course offered by the Division of Applied Mechanics, School of Engineering and the Engineering and Technology Portal
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:
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 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)
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.
Activities:
Readings:
Study guide:
- Wikipedia article:Cartesian coordinates
- Wikipedia article:Polar coordinates
- Wikipedia article:Cylindrical coordinates
- Wikipedia article:Spherical coordinates
- Wikipedia article:Displacement
- Wikipedia article:Distance
- Wikipedia article:Velocity
- Wikipedia article:Speed
- Wikipedia article:Acceleration