PROBLEM 15.195
A 3–in.–radius disk spins at the constant rate
2
4
ω
=
rad/s
about an axis held by a housing attached to a horizontal rod
that rotates at the constant rate
15
ω
=
rad/s. For the position
shown, determine (a) the angular acceleration of the disk,
(b) the acceleration of Point P on the rim of the disk if
θ
= 0,
(c) the acceleration of Point P on the rim of the disk
if
90 .
θ
= °
PROBLEM 15.195 (Continued)
(c)
θ
90 .= °
Acceleration at Point P.
(0.25 ft)
(5 4 ) 0.25
(1.25 ft/s) (1 ft/s)
20 0.25 (5 4 ) ( 1.25 )
0 0 6.25 4 0
P
PP
PP P
=
= ×
=+×
=−+
=× +×
=− × + + ×− +
=+− − +
rj
vr
ik j
ij
aαr v
j j i k ij
jj
ω
ω
2
P= −aj
PROBLEM 15.196
A 3–in.–radius disk spins at the constant rate
2
4
ω
=
rad/s
about an axis held by a housing attached to a horizontal rod
that rotates at the constant rate
1
5
ω
=
rad/s. Knowing that
30 ,
θ
= °
determine the acceleration of Point P on the rim of
the disk.
PROBLEM 15.197
The cone shown rolls on the zx plane with its apex at the origin of
coordinates. Denoting by
ω
1 the constant angular velocity of the axis OB
of the cone about the y axis, determine (a) the rate of spin of the cone
about the axis OB, (b) the total angular velocity of the cone, (c) the
angular acceleration of the cone.
PROBLEM 15.198
At the instant shown, the robotic arm ABC is
being rotated simultaneously at the constant rate
1
0.15
ω
=
rad/s about the y axis, and at the
constant rate
20.25
ω
=
rad/s about the z axis.
Knowing that the length of arm ABC is 1 m,
determine (a) the angular acceleration of the arm,
(b) the velocity of Point C, (c) the acceleration of
Point C.
PROBLEM 15.199
In the planetary gear system shown, gears A and B are
rigidly connected to each other and rotate as a unit about
the inclined shaft. Gears C and D rotate with constant
angular velocities of 30 rad/s and 20 rad/s, respectively
(both counterclockwise when viewed from the right).
Choosing the x axis to the right, the y axis upward, and the
z axis pointing out of the plane of the figure, determine
(a) the common angular velocity of gears A and B, (b) the
angular velocity of shaft FH, which is rigidly attached to
the inclined shaft.
PROBLEM 15.199 (Continued)
PROBLEM 15.200
In Problem 15.199, determine (a) the common angular acceleration of gears A and B, (b) the acceleration of
the tooth of gear A which is in contact with gear C at Point I.
PROBLEM 15.201
Several rods are brazed together to form the robotic guide arm shown
which is attached to a ball–and-socket joint at O. Rod OA slides in a
straight inclined slot while rod OB slides in a slot parallel to the z axis.
Knowing that at the instant shown
(9 in./s) ,
B
=vk
determine (a) the
angular velocity of the guide arm, (b) the velocity of Point A, (c) the
velocity of Point C.
PROBLEM 15.201 (Continued)
Coefficients of j:
( ) 7.5
Ay
v= −
A= −vij
(c) Velocity of C:
542
0.75 1.5 0
5 42
3 1.5 (3 7.5)
C
C
C
=++
= ×
=
=− +−
r ijk
vr
i jk
ij k
ω