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Consider a rigid body which is subjected to either rectilinear or
curvilinear translation in the x-y plane, Fig. 2-15.
Position. The locations of points A and B on the body are
defined with respect to fixed x, y reference frame using position
vectors r and r .The translating x’, y’ coordinate system is fixed in
A
B
the body and has its origin at A, hereafter referred to as the base point.
The position of B with respect to A is denoted by the relative-position
vector r / BA (r of B with respect to A). By vector addition,

r B = r A + r / BA . 2-46
Velocity. A relation between the instantaneous velocities of A
and B is obtained by taking the time derivative of this equation, which
yields v B = v A + dr / BA / dt . Here v and v denote absolute velocities
B
A
since these vectors are measured with respect to the x, y axes. The
0
term dr / BA / dt = since the magnitude of r / BA is constant by
definition of a rigid body, and because the body is translating the
direction of r / BA is also constant. Therefore,

v B = v . 2-47
A
In rectilinear translation, Fig. 2-16,a, all points in the body move
in parallel straight lines. In curvilinear translation, Fig. 2-16,b, all
points move on congruent curves. We note that in each of the two
cases of translation, the motion of the body is completely specified by
the motion of any point in the body, since all points have the same
motion. Thus, our earlier study of the motion of a particle enables us
to describe completely the translation of a rigid body.
Acceleration. Taking the time derivative of the velocity
equation yields a similar relationship between the instantaneous
accelerations of A and B:
a B = a . 2-48
A
The above two equations indicate that all points in a rigid body
subjected to either rectilinear or curvilinear translation move with the
same velocity and acceleration. As a result, the kinematics of particle
motion can also be used to specify the kinematics of particles located
in a translating rigid body.

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