3. The disk rotates about a fixed axis through O with an angular velocity w=5 rad/s

(ccw) and an angular acceleration a=4 rad/s2 (cw) at the instant represented. The

particle A moves in the circular slot with 𝛽 = 2 rad/s (ccw) and 𝛽=3 rad/s2 (cw)

when b=37o. Determine the absolute velocity and acceleration of A at this instant.

Take cos 37=0.8, sin 37=0.6.

Problems (Motion Relative to Rotating Axes)

37o

37o

10 cm

20 cm

A

O

2

1

w1=5 rad/s

C

16 cm

B

OABO

4. Link 1, of the plane mechanism shown, rotates about the fixed point O with

a constant angular speed of 5 rad/s in the cw direction while slider A, at the

end of link 2, moves in the circular slot of link 1. Determine the angular

velocity and the angular acceleration of link 2 at the instant represented

where BO is perpendicular to OA. The radius of the slot is 10 cm.

Take sin 37=06, cos 37=0.8

5. The Geneva wheel is a mechanism for producing intermittent rotation. Pin P

in the integral unit of wheel A and locking plate B engages the radial slots in

wheel C, thus turning wheel C one-fourth of a revolution for each revolution of

the pin. At the engagement position q = 45°. For a constant clockwise angular

velocity w1 = 2 rad/s of wheel A, determine the angular acceleration a2 of wheel

C for the instant when q = 20°.

constant clockwise angular velocity w1 = 2 rad/s, determine the angular acceleration a2 when q = 20°.

O1 O2

P

200 mm

20o

Law of cosines:

dmm42.1412/200

mmd

d

77.82

20cos20042.141220042.141 222

Law of sines:

a

o76.35sin

42.141

20sin

77.82 a

aVelocity

Plate B: jijikrvv

ji

OPOP

79.26574.96sin42.141cos42.1412

37.4889.132

1/11

qqw

1 = 2

1

2

Plate C: jivjikvrvv rel

ji

relOPOP

aaaaww sincossin77.82cos77.82

37.4817.67

22/22

jvivijv relrelP

584.0811.037.4817.67 22 ww

smmvsrad rel /5.234/932.12 w

vrel

O1 O2

P

200 mm

20o

mmd 77.82o76.35a

Acceleration

Plate B:

jiraa OPOP

48.19358.5311/111 ww

3 = 4

3

4

Plate C: relrelOPOPOP avrraa

22/22/222 2waww

22

2 /1.628/59.16 smmasrad rel a

arel

jiajik

jikjikka

rel

v

P

rel

aaaa

a

sincossin5.234cos5.234932.12

37.4817.6737.4817.67932.1932.1 2

jaiajiijjia relrelP

584.0811.016.73452.52937.4817.6755.18072.250 22 aa

arel

6. For the instant shown, particle A has a velocity of 12.5 m/s towards point C relative to

the disk and this velocity is decreasing at the rate of 7.5 m/s each second. The disk rotates

about B with angular velocity w=9 rad/s and angular acceleration a=60 rad/s2 in the

directions shown in the figure. The angle b remains constant during the motion. Telescopic

link has a velocity of 5 m/s and an acceleration of 2.5 m/s. Determine the absolute

velocity and acceleration of point A for the position shown.