Biomedical Engineering Reference
In-Depth Information
Example 2.6
Let the origin of the Cartesian coordinate system be the point with respect to which
the moment vector is computed, i.e.
x
P
=
0.
The point of application of the force vector
F
, is denoted by:
x
Q
=
2
e
x
+
e
y
,
which means that this point is located in the
xy
-plane. The force vector is also
located in this plane:
F
=
e
y
.
The moment of the force
F
with respect to the point P follows from
M
=
5
×
F
x
Q
−
x
P
)
(
=
(2
e
x
+
e
y
)
×
5
e
y
=
10
e
x
×
e
y
+
5
e
y
×
e
y
0
e
z
=
10
e
z
.
Example 2.7
Let, as before:
x
Q
=
e
x
+
e
y
,
2
and
F
=
5
e
y
,
but
x
P
=
3
e
z
.
Then
M
=
(
x
Q
−
x
P
)
×
F
=
(2
e
x
+
e
y
−
3
e
z
)
×
5
e
y
=
10
e
z
+
15
e
x
.
2.11
The two-dimensional case
If all forces act in the same plane, the resulting moment vector with respect to
any point in that plane is, by definition, perpendicular to this plane. However,
