Rigid-Body Planar Equations of Motion
Consider a rigid body as a system of particles:
1)
Translational Equations of Motion:
From section 13.3:
G
a
m
F
=
∑
These are the
translational
equations of motion that state the
sum of all the external forces acting on the body equals the
acceleration of the body’s center-of-mass G.
Scalar equations:
Gy
y
Gx
x
ma
F
ma
F
=
=
∑
∑
2) Rotational Equations of Motion:
Consider the i
th
particle:
where
forces
external
all
of
resultant
F
ns)
interactio
(particle
forces
internal
all
of
resultant
f
i
i
=
=
Summing the moments of force about point P:
i
i
i
i
pi
a
m
r
f
r
F
r
M
×
=
×
+
×
=
0 (when summed over all particles)
=

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