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As shown on the kinematics diagram in Fig. 2-29, the body is
imagined as “extended and pinned” at the IC so that, at the instant
considered, it rotates about this pin with its angular velocity ω.
The magnitude of velocity for each of the arbitrary points A, B
and C on the body can be determined by using the equation v ω= r ,
where r is the radial distance from the IC to each point.
The line of action of each velocity vector v is perpendicular to
its associated radial line r, and the velocity has a sense of direction
which tends to move the point in a manner consistent with the angular
rotation ω of the radial line, Fig. 2-29.

57 Relative-Motion Analysis of Rigid Body: Acceleration

An equation that relates the accelerations of two points on a bar
(rigid body) subjected to general plane motion may be determined by
differentiating v B = v A + v / BA with respect to time. This yields
dv B = dv A + dv / BA . 2-85
dt dt dt
The terms dv B / dt = a and dv A / dt = a are measured with
A
B
respect to a set of fixed x, y, z axes and represent the absolute
accelerations of points B and A. The last term represents the
acceleration of B with respect to A as measured by an observer fixed
to translating ,xy
′′ axes which have their origin at the base point A. In
Sec. 55 it was shown that to this observer point B appears to move
along a circular arc that has a radius of curvature r / BA . Consequently,
a / BA can be expressed in terms of its tangential and normal
) +
) , where (a
components; i.e., a / BA = (a / B A t (a / BA n / B A t α r / BA and
) =
(a / B A n ω 2 r / BA . Hence, the relative acceleration equation can be
) =
written in the form
a B = a A + (a / B A t (a / BA n
) +
) , 2-86
where a - acceleration of point B, a - acceleration of point A,
B
A
(a / B A t
) - tangential acceleration component of B with respect to A and
the direction is perpendicular to r / BA , (a / BA n
) - normal acceleration
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