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 ). Prove the “parallel axis theorem”: The moment of inertia I of a body about a given axis is I = I m + M d 2 , where M is the mass of the body, I m is the moment of inertia of the body about an axis through the center of mass and parallel to the given axis, and d is the distance between the two axes.
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 ). Prove the “parallel axis theorem”: The moment of inertia I of a body about a given axis is I = I m + M d 2 , where M is the mass of the body, I m is the moment of inertia of the body about an axis through the center of mass and parallel to the given axis, and d is the distance between the two axes.
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
).
Prove the “parallel axis theorem”: The moment of inertia I of a body about a given axis is
I
=
I
m
+
M
d
2
, where
M
is the mass of the body,
I
m
is the moment of inertia of the body about an axis through the center of mass and parallel to the given axis, and d is the distance between the two axes.
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