As we have shown, the angular velocity of a rigid Body is
“almost equal” to the angular velocity of any one its’ Body lines
in the sense that if (A, B) ⊆ B, then
ωB = ωAB + ε r B/A ;
ωB ⊥ to AB
ωAB =
r B/A × vB/A
2
L AB
ωB // to AB
expressed in terms of some “εxtra” (+ve, -ve, or perhaps 0-valued)
scalar component value ε. Moreover,
ωB × r B/A
vB/A =
or
ωAB × r B/A
&
r B/A • ωAB = 0
Important Corollary:
The angular velocity of a rigid Body is necessarily parallel to
the line connecting two Body points (A, B) ⊆ B having equal
(identical) velocities
vA = vB
⇒
vA = vB
vB/A = 0 ⇒
⇒
ωAB = 0
ωB = ε r B/A
ωB ∝ r B/A
ωB // line AB
A line drawn through two equal-velocity Body points is referred
to as the Body’s “Omega-Line.”
P.A. Dashner © 2016