
35Newtonian Mechanics
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Differentiating Equation 2.17 once, we obtain
rrV. (2.18)
Thus, if the velocity
of a body P in the frame O is a constant, then its velocity
in the frame O′
is also a constant as shown by Equation 2.18, and the body will obey the law of inertia as observed
in the frame O′.
Differentiating Equation 2.18 once with time, we get
. (2.19)
Thus, the acceleration of the body does not change under Galilean transformations, and we say that
it is a Galilean invariant.
The inertial mass m is unchanged under a Galilean transformation, so
mr
(2.20)
that is, the ma term of ...