The following notation is used in the problems: M = mass , x ¯ , y ¯ , z ¯ = coordinates of center of mass (or centroid if the density is constant), I = moment of inertia (about axis stated), I x , I y , I z = moments of inertia about x, y, z axes, I m = moment of inertia (about axis stated) through the center of mass. Note: It is customary to give answers for I , I m , I x , etc., as multiples of M (for example, I = 1 3 M l 2 ). A rectangular lamina has vertices (0, 0), (0, 2), (3, 0), (3, 2) and density xy. Find (a) M , (b) x ¯ , y ¯ , (c) I x , I y , (d) I m about an axis parallel to the z axis. Hint: Use the parallel axis theorem and the perpendicular axis theorem.
The following notation is used in the problems: M = mass , x ¯ , y ¯ , z ¯ = coordinates of center of mass (or centroid if the density is constant), I = moment of inertia (about axis stated), I x , I y , I z = moments of inertia about x, y, z axes, I m = moment of inertia (about axis stated) through the center of mass. Note: It is customary to give answers for I , I m , I x , etc., as multiples of M (for example, I = 1 3 M l 2 ). A rectangular lamina has vertices (0, 0), (0, 2), (3, 0), (3, 2) and density xy. Find (a) M , (b) x ¯ , y ¯ , (c) I x , I y , (d) I m about an axis parallel to the z axis. Hint: Use the parallel axis theorem and the perpendicular axis theorem.
The following notation is used in the problems:
M
= mass
,
x
¯
,
y
¯
,
z
¯
=
coordinates of center of mass (or centroid if the density is constant),
I
=
moment of inertia (about axis stated),
I
x
,
I
y
,
I
z
=
moments of inertia about x, y, z axes,
I
m
=
moment of inertia (about axis stated) through the center of mass.
Note: It is customary to give answers for
I
,
I
m
,
I
x
, etc., as multiples of M (for example,
I
=
1
3
M
l
2
).
A rectangular lamina has vertices (0, 0), (0, 2), (3, 0), (3, 2) and density xy. Find
(a)
M
,
(b)
x
¯
,
y
¯
,
(c)
I
x
,
I
y
,
(d)
I
m
about an axis parallel to the z axis. Hint: Use the parallel axis theorem and the perpendicular axis theorem.
Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)
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