The acceleration a1
of mass m1
is given by the time derivation
of its linear momentum
p1.
Hence
m1
a1
= dp1/dt =
F21 +
F1,ext
Similarly, is the acceleration a2
of mass m2 given by
m2
a2
= dp2/dt =
F12 +
F2,ext
By using its relation to the total linear momentum
ptotal
of the system of the two masses
and the relation
F21 = - F12,
we find for the acceleration ACM
of the center-of-mass:
( m1 + m2
) ACM =
dptotal/dt =
dp1/dt +
dp2/dt
( m1 + m2
) ACM =
F1,ext +
F2,ext
The acceleration of the center-of-mass is determined
by the total external force on the system.
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