Problems (Motion Relative to Rotating Axes)
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.
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
1
A
10 cm
2
20 cm
37o
C
37o
w1=5 rad/s
O
B
BO  OA
16 cm
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°.
P
200 / 2  141.42 mm
vrel
a
20o
200 mm
O1
d
O2
Law of cosines:
d 2  141.42 2  200 2  2141.42 200  cos 20
d  82.77 mm
Law of sines:
82.77 141.42

sin 20 sin a
Velocity

a  35.76o





 


141.42 cos qi  141.42 sin qj   96.74i  265.79 j 1
Plate B: vP  vO1  w1  rP / O1  2k  




132.89 i  48.37 j





 



Plate C: vP  vO 2  w2  rP / O 2  vrel  w2 k   82.77 cos ai  82.77 sin aj   vrel cos ai  sin aj 






 67.17 i  48.37 j





vP  67.17w2 j  48.37w2 i  0.811vrel i  0.584vrel j 2
1 = 2

w2  1.932 rad / s
vrel  234.5 mm / s
P
d  82.77 mm
a  35.76o
20o
O2
200 mm
O1
arel
Acceleration
Plate B:



 


aP  aO1  w1  w1  rP / O1   531.58i  193.48 j
3

 
 
 



aP  aO 2  w2  w2  rP / O 2   a 2  rP / O 2  2w2  vrel  arel








aP  1.932k  1.932k   67.17i  48.37 j  a 2 k   67.17i  48.37 j





 2 1.932k  234.5 cos ai  234.5 sin aj  arel cos ai  sin aj





vrel









aP  250.72i  180.55 j  67.17a 2 j  48.37a 2 i  529.52i  734.16 j  0.811arel i  0.584arel j 4
Plate C:

3 = 4




a 2  16.59 rad / s 2





arel  628.1 mm / s 2

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.