COSMOS: Complete Online Solutions Manual Organization System
Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,
Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell
© 2007 The McGraw-Hill Companies.
Chapter 15, Solution 1.
Angular coordinate:
(
)2
3
8
6
2
radians
t
t
θ =
−
−
Angular velocity:
(
)
2
24
12
2 rad/s
d
t
t
dt
θ
ω =
=
−
−
Angular acceleration:
2
48
12 rad/s
d
t
dt
ω
α =
=
−
(a) When the angular acceleration is zero.
48
12 0
t −
=
0.250 s
t =
(b) Angular coordinate and angular velocity at t = 0.250 s.
( )(
)
( )(
)
3
2
8 0.250
6 0.250
2
θ =
−
−
18.25 radians
θ = −
(
)(
)
(
)(
)
2
24 0.250
12 0.250
2
ω =
−
−
22.5 rad/s
ω =
COSMOS: Complete Online Solutions Manual Organization System
Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,
Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell
© 2007 The McGraw-Hill Companies.
Chapter 15, Solution 2.
3
0.5
cos4
t
e
t
π
θ
π
−
=
(
)
3
3
0.5 3
cos4
4
sin 4
t
t
d
e
t
e
t
dt
π
π
θ
ω
π
π
π
π
−
−
=
=
−
−
(
)
(
)
2
3
2
3
2
3
2
3
2
3
2
3
0.5 9
cos4
12
sin 4
12
sin 4
16
cos4
0.5 24
sin 4
7
cos4
t
t
t
t
t
t
d
e
t
e
t
e
t
e
t
dt
e
t
e
t
π
π
π
π
π
π
ω
α
π
π
π
π
π
π
π
π
π
π
π
π
−
−
−
−
−
−
=
=
+
+
−
=
−
(a)
0,
t =
(
)
0.5
θ =
0.500 rad
θ =
(
)(
)
0.5
3
4.71
ω
π
=
−
= −
4.71 rad/s
ω = −
(
)(
)
2
0.5
7
34.5
α
π
=
−
= −
2
34.5 rad/s
α = −
( )
0.125 s,
cos4
cos
0,
sin 4
sin
1
2
2
b t
t
t
π
π
π
π
=
=
=
=
=
3
0.30786
t
e
π
−
=
(
)(
)( )
0.5 0.30786 0
0
θ =
=
0
θ =
(
)(
)(
)
0.5 0.30786
4
1.93437
ω
π
=
−
= −
1.934 rad/s
ω = −
(
)(
)(
)
2
0.5 0.30786 24
36.461
α
π
=
=
2
36.5 rad/s
α =
COSMOS: Complete Online Solutions Manual Organization System
Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,
Elliot R. Eisenberg, William E. C