Topic 10
• Kinematics of Rigid Body: Velocity
• Translation
• Rotation about Fixed Axis
• General Plane Motion
• Absolute and Relative Velocity in Plane Motion
• Instantaneous Center of Zero Velocity
Nelson
17.27) A cylinder of 50 cm diameter rolls without slipping on a horizontal plane as shown in
Fig. E.17.27. If the center O of the cylinder moves at a constant speed of 5 m/s, determine (i)
the angular velocity of the cylinder, (ii) the velocities of the points B, C and D on the rim of
the cylinder. (B is the extreme right point, C is the highest point and radial line OD makes an
angle of 45° to the horizontal).
B
A
C
D
O
Fig. E.17.27
17.28) A bar AB of 1.5 m length slides down with its ends in contact with the floor and
vertical wall as shown in Fig. E.17.28. If the end A moves with a constant velocity of 2 m/s
away from the wall, determine (i) angular velocity of the bar, and (ii) the velocity of the end
B.
B
A
40
1.5 m
Fig. E.17.28
17.29) In Fig. E.17.29, if the end A is pushed with a constant velocity of 1 m/s, determine (i)
the angular velocity of the bar, and (ii) the velocity of the end B. At this instant, the bar is
inclined at 60° to the vertical
Fig. E.17.29
17.31) A reciprocating engine mechanism is shown in Fig. E.17.31, in which the crank OA
rotates at a constant angular velocity of 200 rpm in the anticlockwise direction. For the
position shown, determine (i) the angular velocity of the connecting rod AB and (ii) the
velocity of position in the engine. Take OA = 10 cm, AB = 40 cm.
30 β
ω
B
A
O
Fig. E.17.31
17.34) In the four-bar mechanism shown in Fig. E.17.34, the link O1A moves in the anti-
clockwise direction with an angular velocity of 60 rpm. Determine (i) the angular velocity of
links AB and O2B, and (ii) the velocity of the point B. The inclinations of links O1A and O2B
with respective to the horizontal are respectively 60° and 75°
Fig. E.17.34
Extra exercise: To repeat problems 17.28, 17.29, 17.31 and 17.34 but using the
Instantaneous Center of Zero Velocity method
Beer
15.8 The rotor of a gas turbine is rotating at a speed of 6900 rpm when the turbine is shut
down. It is observed that 4 min is required for the rotor to coast to rest. Assuming uniformly
accelerated motion, determine (a) the angular acceleration, (b) the number of revolutions
that the rotor executes before coming to rest.
15.12 The bent rod ABCDE rotates about a line joining points A and E with a constant
angular velocity of 9 rad/s. Knowing that the rotation is clockwise as viewed from E,
determine the velocity and acceleration of corner C.
15.18 The circular plate shown is initially at rest. Knowing that r=200 mm and that the plate
has a constant angular acceleration of 0.3 rad/s2, determine the magnitude of the total
acceleration of Point B when (a) t=0, (b) t=2 s, (c) t=4 s.
15.28 Cylinder A is moving downward with a velocity of 3 m/s when the brake is suddenly
applied to the drum. Knowing that the cylinder moves 6 m downward before coming to rest
and assuming uniformly accelerated motion, determine (a) the angular acceleration of the
drum, (b) the time required for the cylinder to come to rest.
Prob. 15.38
15.38 The motion of rod AB is guided by pins attached at A and B, which slide in the slots
shown. At the instant shown , and the pin at B moves upward to the left with a
constant velocity of 150 mm/s. Determine (a) the angular velocity of the rod. (b) the velocity
of the pin at end A.
15.57 In the engine system shown, l = 160 mm and b = 60 mm. Knowing that the crank AB
rotates with a constant angular velocity of 1000 rpm clockwise, determine the velocity of
the piston P and the angular velocity of the connecting rod when (a) . (b)
15.63 In the position shown, bar AB has an angular velocity of 4 rad/s clockwise. Determine
the angular velocity of bars BD and DE.
Prob. 15.66
15.66 In the position shown, bar DE has a constant angular velocity of 10 rad/s clockwise.
Knowing that h=500mm, determine (a) the angular velocity of bar FBD, (b) the velocity of
Point F.
15.82 Knowing that at the instant shown the angular velocity of rod AB is 15 rad/s clockwise,
determine (a) the angular velocity of rod BD, (b) the velocity of the midpoint of rod BD.
15.86 Knowing that at the instant shown the angular velocity of rod BE is 4 rad/s
counterclockwise , determine (a) the angular velocity of rod AD, (b) the velocity of collar D,
(c) the velocity of Point A.
Bedford
17.2 The angle θ is given as a function of
time by 30.3 0.018t tθ = + rad. At t = 4 s,
determine θ in degrees and the
magnitudes of the velocity and
acceleration of point A.
17.4 At the instant shown, the left disk has an angular velocity of 3 rad/s
counterclockwise and an angular acceleration of 1 rad/s2 clockwise.
(a) What are the angular velocity and
angular acceleration of the right disk?
(Assume that there is no relative motion
between the disks at their point of
contact.)
(b) What are the magnitudes of the
velocity and acceleration of point A?
17.6 (a) If the bicycle’s 120 mm sprocket
wheel rotates through one revolution,
through how many revolutions does the
45 mm gear turn?
(b) If the angular velocity of the sprocket
wheel is 1 rad/s, what is the angular
velocity of the gear?
17.7 The rear wheel of the bicycle has a
330-mm radius and is rigidly attached to
the 45-mm gear. It the rider turns the
pedals, which are rigidly attached to the
120-mm sprocket wheel, at one
revolution per second, what is the
bicycle’s velocity?
17.20 The bracket rotates about the shaft
O with a counterclockwise angular
velocity of 20 rad/s. Determine
(a) the velocity of A relative to B and
(b) the velocity of B relative to A.
17.22 Determine the x and y
components of the velocity of point A.
17.31 Point B is moving to the right at 101.6 m/s. Determine the velocity of point A
and the angular velocity of the bar AB
x
y
17.32 If 45θ = ° and the sleeve P is
moving to the right at 2 m/s, what are
the angular velocities of bars OQ and PQ?
17.34 Bar AB rotates in the
counterclockwise direction at 6 rad/s.
Determine the angular velocity of bar BD
and the velocity of point D.
17.67 Point A and B of the 1-m bar slide
on the plane surfaces. The velocity of B
is vB = 2i (m/s)
(a) What are the coordinates of the
instantaneous center of the bar?
(b) Use the instantaneous center to
determine the velocity of A.
17.68 The bar is in two-dimensional
motion in the x-y plane. The velocity of
point A is vA = 8i (m/s), and B is moving
in the direction parallel to the bar.
Determine the velocity of B
(a) by using B A AB B A
v v rω= + × and
(b) by using the instantaneous center of
the bar.