A Classical Approach of Newtonian Mechanics

4 NEWTON’S LAWS OF MOTION 4.9 Frames of reference

P

O’

O

Figure 34: A moving observer

as

v =

dr

. (4.29)
dt
Hence, the corresponding velocity in the moving observer’s frame of reference
takes the form

vJ^ =

drJ

dt

= v − v 0. (4.30)

Finally, the acceleration of body P in stationary observer’s frame of reference is
defined as

a =

dv
, (4.31)
dt
whereas the corresponding acceleration in the moving observer’s frame of refer-
ence takes the form

aJ^ =

dvJ

dt =^ a.^ (4.32)^

Hence, the acceleration of body P is identical in both frames of reference.

It is clear that if observer O concludes that body P is moving with constant ve-

locity, and, therefore, subject to zero net force, then observer OJ will agree with

this conclusion. Furthermore, if observer O concludes that body P is accelerating,

and, therefore, subject to a force a/m, then observer OJ will remain in agreement.

It follows that Newton’s laws of motion are equally valid in the frames of refer-
ence of the moving and the stationary observer. Such frames are termed inertial

frames of reference. There are infinitely many inertial frames of reference—within

r’^

r

v 0 t