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PROBLEM 18.29
A circular plate of mass
m
is falling with a velocity
0
v
and no angular
velocity when its edge
C
strikes an obstruction. Assuming the impact to be
perfectly plastic
(0),e
determine the angular velocity of the plate
immediately after the impact.
PROBLEM 18.29 (Continued)
Moments about G:
/
222
0()()()
2
111
()( )
424
2
CG G x G y G z
x
yz
Ct H H H
RC t mR mR mR
rjijk
ki i j k
(2)
1
RCt mR
PROBLEM 18.30
For the plate of Problem 18.29, determine (a) the velocity of its mass center
G immediately after the impact, (b) the impulse exerted on the plate by the
obstruction during the impact.
PROBLEM 18.30 (Continued)
Moments about G:
/
0()()()
424
2
CG G x G y G z
Ct H H H
RCt I I I
rjijk
i: 2
1
4
2
x
RCt mR
(3)
1
0
x
xz
R
xz
R
0
22 2( )
zxz
v
R
0
2322
xz
v
R
(6)
Solving Eqs. (5) and (6) simultaneously,
22
xz
v
5
2
yxz
x
yz
vvvvijk
0
4
5v
vj
(b) Impulse at C.
41
5
PROBLEM 18.31
A square plate of side a and mass m supported by a ball-and-socket
joint at A is rotating about the y axis with a constant angular
velocity
0
j
when an obstruction is suddenly introduced at B
in the xy plane. Assuming the impact at B to be perfectly plastic
(e
0),
determine immediately after impact (a) the angular velocity
of the plate, (b) the velocity of its mass center G.
PROBLEM 18.31 (Continued)
Principle of impulse-momentum.
PROBLEM 18.32
Determine the impulse exerted on the plate of Problem 18.31 during
the impact by (a) the obstruction at B, (b) the support at A.
PROBLEM 18.31 A square plate of side a and mass m supported
by a ball-and-socket joint at A is rotating about the y axis with a
constant angular velocity
0
j
when an obstruction is suddenly
introduced at B in the xy plane. Assuming the impact at B to be
perfectly plastic (e
0),
determine immediately after impact (a) the
angular velocity of the plate, (b) the velocity of its mass center G.
PROBLEM 18.32 (Continued)
Principle of impulse-momentum.
Moments about A:
0
()( )( )
AA
aFt
HjkH
0
24 4
y
222
00
111 1
:2 2
yyy
ma ma ma
j
22
11
000
24 32 96
0
( ) 0.1031Ft ma
kk
11
0
00
71
02 2
96 16
tma ma
Akk
12
PROBLEM 18.33
The coordinate axes shown represent the principal centroidal axes of inertia of a 3000-lb space probe whose radii
of gyration are 1.375 ft,
x
k 1.425 ft,
y
k and 1.250 ft.
z
k The probe has no angular velocity when a 5-oz
meteorite strikes one of its solar panels at Point A with a velocity 0(2400 ft/s) (3000 ft/s)
vij
(3200 ft/s)k
relative to the probe. Knowing that the meteorite emerges on the other side of the panel with no change in the
direction of its velocity, but with a speed reduced by 20 percent, determine the final angular velocity of the
probe.
PROBLEM 18.33 (Continued)
Let A
H be the angular momentum of the probe and m
be its mass. Conservation of angular momentum
about the origin for a system of particles consisting of the probe plus the meteorite:
(93.17)(1.375)
x
() 52.41
Ay
H
22
() 52.41
( ) 0.3600 rad/s
Az
zz Az z
H
IH mk
