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Fig. 2-25.

is the vector sum of the translational portion v , plus the rotational
B
portion v / BA = ω r / B A , which has the magnitude v / BA = rω , where
×
ɺ
ωθ= the absolute angular velocity of AB. The fact that the relative
linear velocity is always perpendicular to the line joining the two
points in question is an important key to the solution of many
problems. To reinforce your understanding of this concept, you should
draw the equivalent diagram where point A is used as the reference
point rather than B.
Account for that the relative linear velocity v / BA is always
perpendicular to the line between the two points AB we can draw a
conclusion: the projection of velocity of point B v on the line AB
B
equals the projection of velocity of point A v on the same line.
A
Assume that the angle between the velocity of point A v and
A
the line AB equals α and the angle between the velocity of point B v B
and the line AB equals β . Project equation v B = v A + v / BA on the line
AB, we obtain
v B cosβ = v A cosα + v A/ B cos90°.

Substitute that cos90°= , we can write
0
v A cosα = v B cosβ .
Note, that we projected the vectors of velocity of any two points
on line which draws through these both points.
141