Problem
Set 8: Problem 5.
Problem:
Rod AB is rotating in the counterclockwise direction with constant angular velocity
ω
. Collar
P slides without friction as shown with constant relative speed
u
.
If
r
=
1
2
f
when
θ
= 0
o
and the
collar reaches Point B where
r
=
f
when
θ
= 90
o
, what is collar P’s acceleration vector at the instant
it reaches Point B? Express your answer as a function of
ω
and
f
.
Solution:
We know that in a coordinate frame rotating at angular velocity
Ω
=
ω
k
about Point A, the
collar is not accelerating, i.e.,
a
I
=
0
where
a
I
is the acceleration seen by a rotating observer. In general, the collar’s absolute acceleration is
a
=
a
I
+
˙
Ω
×
r
+ 2
Ω
×
v
I
+
Ω
×
(
Ω
×
r
)
where
v
I
is the collar’s velocity as seen by the rotating observer and
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 Spring '06
 Shiflett
 Acceleration, Angular Momentum, 2 K, Collar, Rod AB

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