PROBLEM 15.187
At the instant considered the radar antenna shown rotates about
the origin of coordinates with an angular velocity
xyz
ωωω
=++
i jk
ω
. Knowing that
( )
15
Ay
v=
in./s,
()
9
By
v=
in./s, and
()
18
Bz
v=
in./s, determine (a) the angular
velocity of the antenna, (b) the velocity of point A.
PROBLEM 15.187 (Continued)
( ) .a Angular velocity
( ) ( ) ( )
0.600 rad/s 2.00 rad/s 0.750 rad/s = −+ij kω
From (1),
( )
10 20.0 in./s
Ay
x
v
ω
=−=
From (3),
()
12 24.0 in./s
Ay
z
v
ω
=−=
( ) . b Velocity of point A
( ) ( ) ( )
20.0 in./s 15.00 in./s 24.0 in./s
A
v=++i jk
Copyright © McGraw–Hill Education. Permission required for reproduction or display.
PROBLEM 15.188
The rotor of an electric motor rotates at the constant rate
1
1800 rpm.
ω
=
Determine the angular acceleration of the rotor as the
motor is rotated about the y axis with a constant angular velocity
2
ω
of 6 rpm counterclockwise when viewed from the positive y axis.
PROBLEM 15.189
The disk of a portable sander rotates at the
constant rate
1
4400 rpm
ω
=
as shown.
Determine the angular acceleration of the disk as
a worker rotates the sander about the z axis with
an angular velocity of 0.5 rad/s and an angular
acceleration of 2.5 rad/s2, both clockwise when
viewed from the positive z axis.
PROBLEM 15.190
A flight simulator is used to train pilots
on how to recognize spatial
disorientation. It has four degrees of
freedom, and can rotate around a
planetary axis as well as in yaw, pitch,
and roll. Knowing that the simulator is
rotating around the planetary axis with
a constant angular velocity of 20 rpm
counterclockwise as seen from above,
determine the angular acceleration of
the cab if (a) the cab has a constant
pitch angular velocity of +3 k rad/s,
(b) the cab has a constant roll angular
velocity of −4 i rad/s.
PROBLEM 15.191
In the system shown, disk A is free to rotate about the horizontal rod
OA. Assuming that disk B is stationary
2
( 0),
ω
=
and that shaft OC
rotates with a constant angular velocity
1
,
ω
determine (a) the angular
velocity of disk A, (b) the angular acceleration of disk A.
PROBLEM 15.192
In the system shown, disk A is free to rotate about the horizontal rod
OA. Assuming that shaft OC and disk B rotate with constant angular
velocities
1
ω
and
2
,
ω
respectively, both counterclockwise, determine
(a) the angular velocity of disk A, (b) the angular acceleration of disk A.
PROBLEM 15.193
The L–shaped arm BCD rotates about the z axis with a constant
angular velocity
1
ω
of 5 rad/s. Knowing that the 150–mm–
radius disk rotates about BC with a constant angular velocity
2
ω
of 4 rad/s, determine (a) the velocity of Point A, (b) the
acceleration of Point A.
PROBLEM 15.194
A gun barrel of length
4 mOP =
is mounted on a turret as
shown. To keep the gun aimed at a moving target, the azimuth
angle
β
is being increased at the rate
/ 30 /sd dt
β
= °
and the
elevation angle
γ
is being increased at the rate
/ 10 /s.
d dt
γ
= °
For the position
β
90= °
and
30 ,
γ
= °
determine (a) the
angular velocity of the barrel, (b) the angular acceleration of
the barrel, (c) the velocity and acceleration of Point P.
PROBLEM 15.194 (Continued)
2(2 3.4641 ) 0
PP P
α
π ππ
=× +×
arv
i jk
ω