Homework set 11, due Wednesday, November 16, 11:30 am
Following problems from Analytical Mechanics by Fowles & Cassiday
1.
8.12
cm
mx
mg
T
=
-
&&
cm
I
aT
ϖ
=
&
cm
x
a
ϖ
=
&&
&
2
2
5
cm
I
ma
=
2
1
2
2
5
5
cm
cm
cm
cm
I
x
mx
mg
mg
ma
mg
mx
a
a
a
ϖ
=
-
=
-
=
-
&
&&
&&
&&
5
7
cm
x
g
=
&&
2.
8.20 (20 points)
mx
mg
μ
=
&&
x
g
μ
=
&&
x
gt
μ
=
&
, and
2
1
2
x
gt
μ
=
2
2
5
I
ma
mga
ϖ
ϖ
μ
=
= -
&
&
5
2
g
a
μ
ϖ
= -
&
5
2
g
t
a
μ
ϖ
ϖ
=
-
o
Slipping ceases to occur when
v
a
ϖ
=
…
5
2
gt
a
gt
μ
ϖ
μ
=
-
o
2
7
a
t
g
ϖ
=
o
2
1
2
2
7
a
x
g
g
ϖ
μ
μ
=
o
2
2
2
49
a
x
g
ϖ
μ
=
o
3.
8.22 (20 points)
From section 8.7 (see Figure 8.7.1), the instantaneous center of rotation is the
point
O
.
If
x
is the distance from the center of mass to
O
and
2
l
is the distance
from the center of mass to the center of percussion
O
′
, then from eqn. 8.7.10 …
a
x
T
r
mg
r
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2
2
1
2
12
12
cm
I
l
Ml
l
x
M
M
=
=
=
6
l
x
=
4.
9.1 (20 points)
9.1
(a)
(
29
2
2
xx
I
y
z
dm
=
+
∫
dm
dxdy
ρ
=
and
2
2
m
a
ρ
=
(
29
2
2
0
0
0
y
a
x
a
xx
y
x
I
y
dxdy
ρ
=
=
=
=
=
+
∫
∫
2
0
2
a
a
y dy
ρ
=
∫
2
4
2
3

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- Fall '08
- Jones,M
- Work, Moment Of Inertia, Trigraph, Perpendicular axis theorem
-
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