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PROBLEM 18.24
Solve Problem 18.23, assuming that the bent rod is hit at
C
.
PROBLEM 18.23
A uniform rod of total mass
m
is bent into the shape shown and is
suspended by a wire attached at
B
. The bent rod is hit at
D
in a direction
perpendicular to the plane containing the rod (in the negative
z
direction). Denoting
the corresponding impulse by
F
t
, determine (
a
) the velocity of the mass center of
the rod, (
b
) the angular velocity of the rod.
PROBLEM 18.24 (Continued)
To determine angular velocity, we shall use Eqs. (18.7) first, we determine the moments & products of
inertia:
12
mmm
2
() ( )
xy
I
aama
22
34
xy
aF t ma ma
(6)
22
11
00
46
xy
ma ma
(7)
000 zz
I
(8)
Multiplying Eq. (7) by 3/2 and adding to Eq. (6):
2,
23 24
38 7
Ft
aF t ma ma
Substituting for
x into (7):
Ft
zz z
Thus: 12 (2 3 )
7
ma
ωij
Note that
y 0, even though Point C where impulse is applied is on the y axis.
PROBLEM 18.25
Three slender rods, each of mass m and length 2a, are welded
together to form the assembly shown. The assembly is hit at A in
a vertical downward direction. Denoting the corresponding
impulse by F,t
determine immediately after the impact (a) the
velocity of the mass center G, (b) the angular velocity of the rod.
PROBLEM 18.25 (Continued)
(b) Angular velocity.
Equate moments about G:
3
zzz z
Therefore,
(3 /8 )( 4 )Ftma
ωik
PROBLEM 18.26
Solve Problem 18.25, assuming that the assembly is hit at
B
in the
negative x direction.
PROBLEM 18.25
Three slender rods, each of mass
m
and length
2
a
, are welded together to form the assembly shown. The
assembly is hit at
A
in a vertical downward direction. Denoting
the corresponding impulse by
F
,
t
determine immediately after
the impact (
a
) the velocity of the mass center
G
, (
b
) the angular
velocity of the rod.
PROBLEM 18.26 (Continued)
(b) Angular velocity.
Equate moments about G:
(3 /8 )( 4 )Ftma
ωjk
PROBLEM 18.27
Two circular plates, each of mass 4 kg, are rigidly connected by
a rod
AB
of negligible mass and are suspended from Point
A
as
shown. Knowing that an impulse
(2.4 N s)t
Fk
is
applied at Point
D
, determine (
a
) the velocity of the mass center
G
of the assembly, (
b
) the angular velocity of the assembly.
PROBLEM 18.27 (Continued)
(a) Direct components:
2tmFv
0 2 0
xx
mv v
2(2)(4)
z
(b) Moments about G. ()( )
G
br Ft
j
ikH
x
y
: (0.18)(2.4) ( 0.216) 0.3888
x
y
j
(2)
k: 0 0.504 0
zz
PROBLEM 18.28
Two circular plates, each of mass 4 kg, are rigidly connected by
a rod
AB
of negligible mass and are suspended from Point
A
as
shown. Knowing that an impulse
(2.4 N s)t
Fj
is applied
at Point
D
, determine (
a
) the velocity of the mass center
G
of
the assembly, (
b
) the angular velocity of the assembly.
PROBLEM 18.28 (Continued)
(a) Direct components:
2tm
Fv
0 2 0
xx
mv v
zz
Point A moves upward. The cord becomes slack. ()0Tt
2.4 0.300 m/s
(2)(4)
y
v (0.300 m/s)vj
x
xxyy xyxyy zz
Resolve into components and apply the numerical data.
: (0.18)(2.4) 0.2448 ( 0.216)
x
y
i (1)
:j 0 ( 0.216) 0.3888
x
y
(2)
