PROBLEM 15.8
The angular acceleration of an oscillating disk is defined by the relation
.
k
αθ
= −
Determine (a) the value of
k for which
12
ω
=
rad/s when
0
θ
=
and
6
θ
=
rad when
0,
ω
=
(b) the angular velocity of the disk when
3
θ
=
rad.
PROBLEM 15.9
The angular acceleration of a shaft is defined by the relation
0.5 ,
αω
= −
where
α
is expressed in
2
rad/s
and
ω
in rad/s. Knowing that at
0t=
the angular velocity of the shaft is 30 rad/s, determine (a) the number
of revolutions the shaft will execute before coming to rest, (b) the time required for the shaft to come to rest,
(c) the time required for the angular velocity of the shaft to reduce to 2 percent of its initial value.
PROBLEM 15.10
The bent rod ABCDE rotates about a line joining Points A and
E with a constant angular velocity of 9 rad/s. Knowing that
the rotation is clockwise as viewed from E, determine the
velocity and acceleration of corner C.
PROBLEM 15.11
In Problem 15.10, determine the velocity and acceleration of
corner B, assuming that the angular velocity is 9 rad/s and
increases at the rate of
2
45 rad/s .
PROBLEM 15.10 The bent rod ABCDE rotates about a line
joining Points A and E with a constant angular velocity of 9
rad/s. Knowing that the rotation is clockwise as viewed from
E, determine the velocity and acceleration of corner C.
PROBLEM 15.12
The rectangular block shown rotates about the diagonal OA with a constant
angular velocity of 6.76 rad/s. Knowing that the rotation is counterclockwise
as viewed from A, determine the velocity and acceleration of point B at the
instant shown.
PROBLEM 15.13
The rectangular block shown rotates about the diagonal OA with an
angular velocity of 3.38 rad/s that is decreasing at the rate of 5.07
2
rad/s .
Knowing that the rotation is counterclockwise as viewed from A,
determine the velocity and acceleration of point B at the instant shown.
PROBLEM 15.13 (Continued)
Acceleration of point B:
/B BO B
=× +×
ar vαω
0.75 4.68 1.8 0.5 3.12 1.2
5 15.6 0 18.72 6 7.8
B
=− −−+
−−
i j k i jk
a
28.08 9 11.7 31.536 18.564 61.406= −+ − − +ij k i j k
() ( ) ( )
222
3.46 in./s 27.6 in./s 73.1in./s
B
=−− +a i jk
PROBLEM 15.14
A circular plate of 120 mm radius is supported by two
bearings A and B as shown. The plate rotates about the
rod joining A and B with a constant angular velocity of
26 rad/s. Knowing that, at the instant considered, the
velocity of Point C is directed to the right, determine the
velocity and acceleration of Point E.
PROBLEM 15.15
In Problem 15.14, determine the velocity and acceleration of Point E, assuming that the angular velocity is
26 rad/s and increases at the rate of 65 rad/s2.
PROBLEM 15.16
The earth makes one complete revolution around the sun in 365.24 days. Assuming that the orbit of the earth
is circular and has a radius of 93,000,000 mi, determine the velocity and acceleration of the earth.