PROBLEM 16.161
A cylinder with a circular hole is rolling without slipping on a
fixed curved surface as shown. The cylinder would have a weight
of 16 lb without the hole, but with the hole it has a weight of
15 lb. Knowing that at the instant shown the disk has an angular
velocity of 5 rad/s clockwise, determine (a) the angular
acceleration of the disk, (b) the components of the reaction force
between the cylinder and the ground at this instant.
PROBLEM 16.161 (Continued)
Point C is the instantaneous center, so that
A
r
ω
=v
Point A is constrained to move on a circle of radius
Rr
r
= +
PROBLEM 16.161 (Continued)
It remains to determine the distance b from the mass distribution of the cylinder.
The mass center G coincides with the centroid of a circular cylinder of area
2
1
Ar
π
=
with a circular cut out of
1
2
PROBLEM 16.162
The motion of a square plate of side 150 mm and mass 2.5 kg is guided
by pins at corners A and B that slide in slots cut in a vertical wall.
Immediately after the plate is released from rest in the position shown,
determine (a) the angular acceleration of the plate, (b) the reaction at
corner A.
PROBLEM 16.162 (Continued)
Law of sines.
//
0.707
sin15 sin 0.25950
GA GA
aa
aL
aL
a
βa
°
sin 0.707; 135
ββ
= = °
0.2583L
a
=a
45°
Kinetics:
( 0)
ω
=
We find the location of Point E where lines of action of A and B intersect.
2
15
L
MG
EAG
=
= °
( ) 0.6829 0.5 0.183
( ) (0.183 ) 2 0.2588
y
EG L L L
EG L L
= −=
= =
2
1
6
I mL
=
PROBLEM 16.162 (Continued)
(a) Angular acceleration.
eff
( ) : (0.183 ) ( )(0.2588 )
AA
M M mg L I ma L
a
Σ=Σ =+
2
2
1
0.183 (0.2588 )(0.2588 )
6
1
mgL mL m L L
aa
= +
PROBLEM 16.163
Solve Problem 16.162, assuming that the plate is fitted with a single pin
at corner A.
Problem 16.162 The motion of a square plate of side 150 mm and mass
2.5 kg is guided by pins at corners A and B that slide in slots cut in a
vertical wall. Immediately after the plate is released from rest in the
position shown, determine (a) the angular acceleration of the plate,
(b) the reaction of corner A.
PROBLEM 16.163 (Continued)
(a) Angular acceleration.
eff
( ) : ( )sin15 ( )sin15
AA
M M mg AG I ma AG
a
Σ =Σ °= + °
2
2
1
sin15 (0.183 ) sin15
6
22
1
0.183 0.033494
6
0.183 0.2002
0.9143
9.81m/s
LL
mg mL m L
g
L
g
Lg
L
aa
a
a
a
°= + °
= +
=
=
2
PROBLEM 16.164
The Geneva mechanism shown is used to provide an intermit-
tent rotary motion of disk S. Disk D weighs 2 lb and has a
radius of gyration of 0.9 in. and disk S weighs 6 lb and has a
radius of gyration of 1.5 in. The motion of the system is
controlled by a couple M applied to disk D. A pin P is attached
to disk D and can slide in one of the six equally spaced slots
cut in disk S. It is desirable that the angular velocity of disk S
be zero as the pin enters and leaves each of the six slots; this
will occur if the distance between the centers of the disks and
the radii of the disks are related as shown. Knowing disk D
rotates with a constant counterclockwise angular velocity of 8
rad/s and the friction between the slot and pin P is negligible,
determine when
φ
= 150° (a) the couple M, (b) the magnitude
of the force pin P applies to disk S.
PROBLEM 16.164 (Continued)
Motion of disk D. (rotation about B)
( ) (1.25)(8) 10 in./s
PD
BP
ω
= = =v
30°
[( )
PD
BP
a
=a
2
60 ] [( ) S
BP
ω
°+
2
30 ] 0 [(1.25)(8)
°= +
30 ]°
2