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an observer in India, the strip mall that constituted the frame of reference in
panel (b) of the figure was moving along with the earth’s rotation at hun-
dreds of miles per hour.
The reason why Newton’s laws fail in the truck’s frame of reference is
not because the truck is moving but because it is accelerating. (Recall that
physicists use the word to refer either to speeding up or slowing down.)
Newton’s laws were working just fine in the moving truck’s frame of
reference as long as the truck was moving at constant velocity. It was only
when its speed changed that there was a problem. How, then, are we to tell
which frames are accelerating and which are not. What if you claim that
your truck is not accelerating, and the sidewalk, the asphalt, and the Burger
King are accelerating. The way to settle such a dispute is to examine the
motion of some object, such as the bowling ball, which we know has zero
total force on it. Any frame of reference in which the ball appears to obey
Newton’s first law is then a valid frame of reference, and to an observer in
that frame, Mr. Newton assures us that all the other objects in the universe
will obey his laws of motion, not just the ball.
Valid frames of reference, in which Newton’s laws are obeyed, are called
inertial frames of reference. Frames of reference that are not inertial are called
noninertial frames. In those frames, objects violate the principle of inertia
and Newton’s first law. While the truck was moving at constant velocity,
both it and the sidewalk were valid inertial frames. The truck became an
invalid frame of reference when it began changing its velocity.
You usually assume the ground under your feet is a perfectly inertial
frame of reference, and we made that assumption above. It isn’t perfectly
inertial, however. Its motion through space is quite complicated, being
composed of a part due to the earth’s daily rotation around its own axis, the
monthly wobble of the planet caused by the moon’s gravity, and the rota-
tion of the earth around the sun. Since the accelerations involved are
numerically small, the earth is approximately a valid inertial frame.
Noninertial frames are avoided whenever possible, and we will seldom,
if ever, have occasion to use them in this course. Sometimes, however, a
noninertial frame can be convenient. Naval gunners, for instance, get all
their data from radars, human eyeballs, and other detection systems that are
moving along with the earth’s surface. Since their guns have ranges of many
miles, the small discrepancies between their shells’ actual accelerations and
the accelerations predicted by Newton’s second law can have effects that
accumulate and become significant. In order to kill the people they want to
kill, they have to add small corrections onto the equation a=F
total
/m. Doing
their calculations in an inertial frame would allow them to use the usual
form of Newton’s second law, but they would have to convert all their data
into a different frame of reference, which would require cumbersome
calculations.
Discussion question
If an object has a linear x-t graph in a certain inertial frame, what is the effect
on the graph if we change to a coordinate system with a different origin. What
is the effect if we keep the same origin but reverse the positive direction of the
x axis. How about an inertial frame moving alongside the object. What if we
describe the object’s motion in a noninertial frame.
Section 4.5Inertial and Noninertial Frames of Reference