ab and the velocity of center of disk e. use the...

1. The disk D rolls to the left without slipping and has an angular velocity of 3 rad/s. Determine the angular

velocity of link AB and the velocity of center of disk E. Use theMethod of Instantaneous Center of Zero Velocity.

60o

w=3 rad/s

45o

R

R

0.4 m

0.3 m

3R

A

B

D E

R=0.5 m

O1 O2

Instantaneous Center of Zero Velocity

2. The mechanism used in a marine engine consists of a single crank AB and twoconnecting rods BC and BD. Determine the velocity of the pistons at C and D andangular velocities of rods BC and BD when the crank is in the position shown and hasan angular velocity of 5 rad/s.

s/m.ABv ABB 1205 w

Cv

Dv

P2 (IC of link BD)

P1 (IC of link BC)

Instantaneous Center of Zero Velocity

0.5 m

s/m.v

ABv

B

ABB

1205

w

Cv

Dv

P2 (IC for link BD)

P1 (IC for link BC)

P2

D

B

30o

105o

45o

0.6

83

m

s/m.v

s/rad.

.

v

.

v

m.DP

m.BP

sin

DP

sin

BP

sin

.

D

BD

DBBD

5180

4641

35406830

1

3540

6830

3010545

50

2

2

22

w

w

P1

C

B60o

75o

45o

0.5

46

m

s/m.v

s/rad.

.

v

.

v

m.BP

m.CP

sin

BP

sin

CP

sin

.

D

BC

CBBC

8960

83151

48905460

1

5460

4890

756045

40

1

1

11

w

w

0.5 m

Motion Relative to Rotating Axes

4. The gear has the angular motion shown. Determine the angular velocity and angular

acceleration of the slotted link BC at this instant. The pin at A is fixed to the gear.

w=2 rad/s

a=4 rad/s20.5 m

0.7 m

2 m

O

B

A C

Motion Relative to Rotating Axes

Kinetics of Rigid Bodies

wAB=w1=10 rad/s (cw)wBC=2.5 rad/s (ccw)aBC=21.09 rad/s2 (ccw)ac=21.204 m/s2 (↑)

5. A compressor is shown in the figure. Member AB is rotating at a constant angular

velocity of 10 rad/s. Member BC has a mass of 2 kg and piston C has a mass of 1 kg. The

pressure p on the circular surface of the piston is 10 kPa. At the instant shown, what are the

forces transmitted by pins B and C?

6. The unbalanced 20 kg wheel with the mass center at G has a radius of gyration

about G of 202 mm. The wheel rolls down the 20o incline without slipping. In the

position shown. The wheel has an angular velocity of 3 rad/s. Calculate the friction

force F acting on the wheel at this position.

“General Motion”FBD

N

mg

Ff

KD

=

am

aI

222

8160202020 mkg.).(kmI

aa 25.0 raox x

y

j.i..i.kki.ki.aaa

yx

aa

O/GOG

075067502500750330750250 aaa

604805

67502502020

.F

..FsinmgamF

f

fxefx

a

a

a

a51367184

07502020

..N

.cosmgNamF yefy

aa 81602500750 .).(F).(NIM fefGN.N

N.F

s/rad.

f

971160

6172

59715 2

a❷

❸

❶