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 triangular lamina has vertices (0, 0), (0, 6) and (6, 0), and uniform density. Find: (a) x ¯ , y ¯ , (b) I x , (c) I m about an axis parallel to the x axis. Hint: Use Problem 1 carefully
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 triangular lamina has vertices (0, 0), (0, 6) and (6, 0), and uniform density. Find: (a) x ¯ , y ¯ , (b) I x , (c) I m about an axis parallel to the x axis. Hint: Use Problem 1 carefully
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 triangular lamina has vertices (0, 0), (0, 6) and (6, 0), and uniform density. Find:
(a)
x
¯
,
y
¯
,
(b)
I
x
,
(c)
I
m
about an axis parallel to the x axis. Hint: Use Problem 1 carefully
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