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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.