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.