Problem 17.116 The large gear is fixed. The angu-
lar velocity and angular acceleration of the bar AB are
ωAB =2 rad/s and αAB =4 rad/s2. Determine the angu-
lar acceleration of the bars CD and DE.
4 in 16 in
BCD
10 in
vD=vC+ωCD ×rCD =−28i+28j+
ij k
00ωCD
−10 14 0
=−14ωDEi−10ωDEj(in/s).
Equate and separate components:
16 0 0
aD=−396i+(16αCD +56)j(in/s2).
Equate the expressions for aDand separate components:
−396 =40 −14αDE,16αCD +56 =−10αDE −56.
Problem 17.117 In Active Example 17.7, suppose that
the distance from point Cto the pin Aon the vertical bar
AC is 300 mm instead of 400 mm. Draw a sketch of the
velocity of the bar AC and the velocity of the pin A
relative to the slot in bar AB.
400 mm
10 rad/s2
A
Problem 17.118 The bar rotates with a constant
counterclockwise angular velocity of 10 rad/s and sleeve
Aslides at a constant velocity of 4 ft/s relative to the
Solution: Eq. (17.15) is
aA=aB+aArel +2ω×vArel +α×rA/B −ω2rA/B .
ij k
Problem 17.119 Sleeve Cslides at 1 m/s relative to
bar BD. Use the body-fixed coordinate system shown to
determine the velocity of C.
Solution: The velocity of point Bis
ijk
414
Problem 17.120 In Problem 17.119, the angular accel-
erations of the two bars are zero and the sleeve Cslides
at a constant velocity of 1 m/s relative to bar BD . What
is the acceleration of C?
1 m/s
C
DB
4 rad/s
y
x
BDrC/B.
Problem 17.121 Bar AC has an angular velocity
of 2 rad/s in the counterclockwise direction that is
decreasing at 4 rad/s2. The pin at Cslides in the slot
in bar BD.
(a) Determine the angular velocity of bar BD and the
(b) Determine the angular acceleration of bar BD and
the acceleration of the pin relative to the slot.
D
C
74 0
vC=vB+vCrel +ωBD ×rC/B
Equating iand jcomponents in Eqs. (5) and (6),
Problem 17.122 In the system shown in Prob-
lem 17.121, the velocity of the pin Crelative to the slot
is 21 in/s upward and is decreasing at 42 in/s2.What are
the angular velocity and acceleration of bar AC?
4 in
D
C
BA
(4), (7), and (8) with vCrel =21 in/s and aCrel =−42 in/s2, we obtain
Problem 17.123 In the system shown in Prob-
lem 17.121, what should the angular velocity and accel-
eration of bar AC be if you want the angular velocity and
acceleration of bar BD to be 4 rad/s counterclockwise
and 24 rad/s2counterclockwise, respectively?
(4), (7), and (8) with ωBD =4 rad/s2and αBD =24 rad/s2, we obtain
Problem 17.124 Bar AB has an angular velocity of
4 rad/s in the clockwise direction. What is the velocity
of pin Brelative to the slot?
B
60 mm
416
Problem 17.125 In the system shown in Prob-
lem 17.124, the bar AB has an angular velocity of
4 rad/s in the clockwise direction and an angular accel-
eration of 10 rad/s2in the counterclockwise direction.
What is the acceleration of pin Brelative to the slot?
B
60 mm
Problem 17.126 The hydraulic actuator BC of the
crane is extending (increasing in length) at a constant
rate of 0.2 m/s. At the instant shown, what is the angular
velocity of the crane’s boom AD?
Strategy: Use Eq. (17.8) to write the velocity of point
Cin terms of the velocity of point A, and use Eq. (17.11)
to write the velocity of point Cin terms of the velocity
of point B. Then equate your two expressions for the
velocity of point C.
1.8 m 1.2 m
B
C
2.4 m
1 m
A
D
Solution: Using Bar ACD
vC=vA+ωAD ×rC/A =0+ωAD k×(3i+1.4j)m
Problem 17.127 In Problem 17.126, what is the
angular acceleration of the crane’s boom AD at the
instant shown?
1.8 m 1.2 m
C
A
D
Solution: Use the angular velocities from 17.126
Bar ACD
aC=aA+αACD ×rC/A −ωACD 2rC/A
=0+αACD k×(3i+1.4j)m−ωACD 2(3i+1.4j)m
418
Problem 17.128 The angular velocity ωAC =5◦per
second. Determine the angular velocity of the hydraulic
actuator BC and the rate at which the actuator is
extending.
2.4 m
1.2 m1.4 m
AB
C
aAC
vAC
Solution: The point Ceffectively slides in a slot in the arm BC.
Problem 17.129 In Problem 17.128, if the angular
velocity ωAC =5◦per second and the angular
acceleration αAC =−2◦per second squared, determine
the angular acceleration of the hydraulic actuator BC
and the rate of change of the actuator’s rate of extension.
2.4 m
C
aAC
vAC
Solution: Use the solution to Problem 17.128 for the velocities:
ωBC =0.1076 rad/s,
The acceleration of point Cin terms of the hydraulic actuator is
420
Problem 17.130 The sleeve at Aslides upward at a
constant velocity of 10 m/s. Bar AC slides through the
sleeve at B. Determine the angular velocity of bar AC
and the velocity at which the bar slides relative to the
sleeve at B. (See Example 17.8.)
10 m/s
Solution: The velocity of the sleeve at Ais given to be vA=
vA=(0.866i+0.5j)vArel +ωAC (−0.5i+0.866j)(m/s).
The given velocity is vA=10j(m/s). Equate like components in the
two expressions for vA:
0=0.866vArel −0.5ωAC ,
10 =0.5vArel +0.866ωAC .
Solve: ωAC =8.66 rad/s (counterclockwise),
vArel =5 m/s from Btoward A.
C
B
A
y
x
Problem 17.131 In Problem 17.130, the sleeve at A
slides upward at a constant velocity of 10 m/s. Deter-
mine the angular acceleration of bar AC and the rate of
change of the velocity at which the bar slides relative to
0.866 0.50
0=(0.866i+0.5j)aArel −43.3i+75j
+αAB(−0.5i+0.866j)−64.95i−37.5j.
Problem 17.132 Block Aslides up the inclined surface
at 2 ft/s. Determine the angular velocity of bar AC and
the velocity of point C.
B
x
2 ft 6 in
y
2 ft 6 in4 ft 6 in
20⬚
A
C
422
Problem 17.133 In Problem 17.132, block Aslides up
the inclined surface at a constant velocity of 2 ft/s.
Determine the angular acceleration of bar AC and the
acceleration of point C.
B
x
2 ft 6 in
y
2 ft 6 in4 ft 6 in
20⬚
A
C
Problem 17.134 The angular velocity of the scoop is
1 rad/s clockwise. Determine the rate at which the hy-
draulic actuator AB is extending.
1 ft 6 in
2 ft
C
B
DE
A
424
Problem 17.135 The angular velocity of the scoop is
1 rad/s clockwise and its angular acceleration is zero.
Determine the rate of change of the rate at which the
hydraulic actuator AB is extending. 1 ft 6 in
2 ft 6 in
5 ft
2 ft
C
B
DE
A
0.5ω2
BC)=(αBD −2ω2
BD). From the solution to Problem 17.134,
Problem 17.136 Suppose that the curved bar in
Example 17.9 rotates with a counterclockwise angular
velocity of 2 rad/s.
(a) What is the angular velocity of bar AB?
(b) What is the velocity of block Brelative to the slot?
350 mm
500
mm
AC
B
1 rad/s
D
426
Problem 17.137 Suppose that the curved bar in
Example 17.9 has a clockwise angular velocity of
4 rad/s and a counterclockwise angular acceleration of
10 rad/s2. What is the angular acceleration of bar AB?350 mm
500
mm
AC
B
1 rad/s
Problem 17.138* The disk rolls on the plane surface
with a counterclockwise angular velocity of 10 rad/s.
Bar AB slides on the surface of the disk at A. Determine
A
B
C
2 ft
10 rad/s
45⬚
β=sin−1sin 45◦
428
Problem 17.139* In Problem 17.138, the disk rolls on
the plane surface with a constant counterclockwise angu-
lar velocity of 10 rad/s. Determine the angular acceler-
ation of bar AB.
A
B
C
2 ft
10 rad/s
1 ft
45⬚
Solution: Use the results of the solution to Problem 17.138.
The acceleration of point Ain terms of the disk is
Problem 17.140* Bar BC rotates with a counterclock-
wise angular velocity of 2 rad/s. A pin at Bslides in a
circular slot in the rectangular plate. Determine the angu-
lar velocity of the plate and the velocity at which the pin
slides relative to the circular slot.
AB
430
Problem 17.141* Bar BC in Problem 17.140 rotates
with a constant counterclockwise angular velocity of
2 rad/s. Determine the angular acceleration of the plate.
AB
40 mm
40 mm
30 mm
C
60 mm
Solution: Choose the same coordinate system as in Problem
The acceleration of the pin in terms of the plate AB is
Problem 17.142* By taking the derivative of
Eq. (17.11) with respect to time and using Eq. (17.12),
derive Eq. (17.13).
Solution: Eq (17.11) is
432