8.3. EQUATIONS OF MOTION OF RIGID BODIES IN 2D SPACE 151
Similarly, total bearing force at B,
F
TB
D
q
F
B
C F
0
B
2
C F
2
12
N
D
q
20;72598
2
C
.
4259:77
/
2
N
D 21;159:20 N:
e forces and directions are illustrated in Figure 8.8b.
8.3 EQUATIONS OF MOTION OF RIGID BODIES IN 2D
SPACE
Having obtained the equations of motion for rigid bodies in 3D space, it is relatively straight
forward to simplify them for rigid body motion in 2D space or commonly called planar motion
of rigid bodies.
Consider the 2D rigid body, shown in Figure 8.9 and by making use of Equations (8.2)
as well as (8.12c), one obtains
n
X
iD1
.
F
i
/
x
D m
.
a
G
/
x
;
n
X
iD1
.
F
i
/
y
D m
.
a
G
/
y
;
n
X
iD1
.
M
G
/
z
i
D
N
I ˛; (8.24)
where
N
I is the moment of inertia of the rigid body about an axis perpendicular to the plane of
the 2D rigid body and through the mass center G. Equations in (8.24) state that the motion of
the 2D rigid body is completely defined by the resultant and moment resultant about mass center G of
the external forces exerting on it.
F
⃑
1
F
⃑
5
F
⃑
4
F
⃑
3
F
⃑
2
Y
O
X
G
°
G°
=
ma⃑
I
̅
α⃑
Figure 8.9: A rigid body in 2D space.
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