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PROBLEM 16.157
The uniform rod AB of weight W is released from rest when
70 .
β
= °
Assuming that the friction force between end A and the surface is large
enough to prevent sliding, determine immediately after release (a) the
angular acceleration of the rod, (b) the normal reaction at A, (c) the
friction force at A.
PROBLEM 16.157 (Continued)
For
70 :
β
= °
3 cos70
2
g
L
°
L
(b) Eq. (3):
2
3
1 cos 70
4
A
N mg
=−°
0.912
A
mg
=N
(c) Eq. (2)
3sin70 cos70
4
A
F mg= °°
0.241
A
mg=F
PROBLEM 16.158
The uniform rod AB of weight W is released from rest when
70 .
β
= °
Assuming that the friction force is zero between end A and the surface,
determine immediately after release (a) the angular acceleration of the
rod, (b) the acceleration of the mass center of the rod, (c) the reaction at A.
PROBLEM 16.158 (Continued)
2
22
6 cos cos
22
1 3cos 1 3cos
L Lg g
L
ββ
ββ
++
22
6 cos 1 1
6 cos 6 cos
1 3cos 1 3cos
mL mL g mg
L
aβ
ββ
ββ
=⋅ =⋅⋅ =
++
A
(a)
2
6 cos70
1 3cos 70
g
L
a
°
=+°
1.519 g
L
=a
2
2
cos 70
(c)
2
1
1 3cos 70
A mg=+°
0.740mg=A
PROBLEM 16.159
A bar of mass
5 kg
m=
is held as shown between
four disks, each of mass
2 kg
m′=
and radius
75 mm.r=
Knowing that the normal forces on the
disks are sufficient to prevent any slipping, for each
of the cases shown determine the acceleration of the
bar immediately after it has been released from rest.
PROBLEM 16.159 (Continued)
Kinetics of bar
( ):
FF
Σ=Σ
Kinetics of one disk
2
1
2
I mr
′
=
( ):
MMΣ=Σ
PROBLEM 16.159 (Continued)
Substitute for F from (2) into (1):
64
mg m a m g ma
′′
−+=
PROBLEM 16.160
A uniform plate of mass m is suspended in each of the ways shown. For each case determine immediately
after the connection at B has been released (a) the angular acceleration of the plate, (b) the acceleration of its
mass center.
PROBLEM 16.160 (Continued)
(b) From (1):
11
(1.2 ) 0.3
44
xx
ac g g
a
= = =a
11
22
(2) Plate suspended from wires.
Kinematics: Assume
a
( 0)
=ω
/C A GA
= = +aa a a
A
ar
a
= ↔+
θ
y comp.
0 cos
( cos )
y
ar
r
aθ
θa
= −
= −
1
Thus:
11
22
yy
ac c
aa
=−=a
(2)
Kinetics:
2
22
1
12 2 48
cI
I m c mc
= +=
PROBLEM 16.160 (Continued)
(3) Plate suspended from springs. Immediately after spring B is released, the tension in spring A is still
1
2mg
since its elongation is unchanged.
(a) Angular acceleration.
11
