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By using Eq. 2-77, we can define both module and direction of
vector of Coriolis acceleration. According to vector cross product we
have a formula
)
,
v
a =Ω tr sin (Ω v . 2-78
2
t
C
r
The magnitude of Coriolis acceleration equals double
product of the magnitude of translation angular velocity Ω , the
t
magnitude of relative linear velocity v and sine of angle between
r
their vectors.
According to Eq. 2-78, Coriolis acceleration equals zero in
following cases:
0
1) the moving reference system does not rotate, Ω= ;
t
2) the particle B does not move relation to the moving x, y, z
0
reference frame, v = ;
r
3) the vector of relative linear velocity is parallel to the rotating
axes of moving reference frame (v  Ω ), mathematically
t
r
,
sin (Ω v r ) 0= .
t
The direction of Coriolis acceleration is determined by the right-
hand rule: that is, the sense of rotation is indicated by the curl of the
fingers, and the thumb is directed along the Coriolis acceleration. The
vector Coriolis acceleration is normal to plane, which includes vectors
translation angular velocity and relative linear velocity.
XII RELATIVE-MOTION ANALYSIS OF RIGID BODY
54 General Plane Motion of A Rigid Body
The general plane motion of a rigid body can be described as a
combination of translation and rotation. To view these “component”
motions separately we will use a relative-motion analysis involving
two sets of coordinate axes. The x, y coordinate system is fixed and
measures the absolute position of two points A and B on the body,
here represented as a bar, Fig. 2-22. The origin of the x', y' coordinate
system will be attached to the selected “base point” A, which generally
has a known motion. The axes of this coordinate system translate with
respect to the fixed frame but do not rotate with the bar.

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