Inertial Reference Frames
K. McWilliams
Inertial Reference Frames
Inertia is the tendency of an object to resist changes in its motion. Inertia is
quantified by mass:
large mass ↔ large inertia
small mass ↔ small inertia
An inertial reference frame is a reference frame in which Newton's 2nd Law (and
therefore Newton's 1st law) is valid, i.e., a reference frame that is not accelerating.
Example 1:
A traffic light turns green. The driver steps on the gas, accelerating. Dice
hanging from the rear-view mirror swing towards the back of the car. Relative to
the car itself, Newton's 1st law is not valid, i.e., inside the car is not an inertial
reference frame. At one moment, the dice are hanging straight down, then
suddenly they move back. Inside the car, there is no causal force. BUT, if you
were watching from the sidewalk, the dice would remain stationary with respect
to you until tension in the string (i.e., a force) holding them to the rear-view
mirror pulls the dice forward, along with the car. So on the sidewalk, you can
observe the force causing the change in motion, as well as the resulting motion.
The sidewalk IS an inertial reference frame in this case. SO, Newton's 1st law is
true from the sidewalk, but not inside the car.
Example 2:
If a driver, cruising along at 100 km per hour, slams on the brakes, the dice swing
forward. Inside the car is NOT an inertial reference frame. An observer on the
side of the road IS in an inertial reference frame.
Example 3:
If a driver turns to the left, the dice will swing to the right. Again, inside the car is
NOT an inertial reference frame. An observer on the side of the road IS in an
inertial reference frame.
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Inertial Reference Frames
K. McWilliams
Example 4:
Now, you are inside a car moving at 100 km per hour (constant velocity). The
dice are hanging straight down when viewed by someone inside the car, i.e., the
dice appear stationary relative to a passenger in the car. Someone standing on the
side of the road also sees the dice hanging straight down and passing by at 100
km/h. To both observers the principle of inertia is true. The dice are stationary
for a passenger in the car (they do not change their velocity). The dice are
moving at a constant velocity when viewed from the side of the road (they are
moving along at a constant speed of 100 km/h). In this case, both reference
frames are inertial reference frames. The important thing here is that the dice are
moving at a CONSTANT SPEED, i.e., there is NO ACCELERATION.
Example 5:
I am inside a car that is stopped, waiting for the traffic light to turn green, and I
push on the dice with my hand. I am applying a force, and the dice swing in the
direction that I push them. BOTH inside the car and the side of the road ARE
inertial reference frames in this case. The CAUSE and the EFFECT are observed
in both reference frames.
Classic Example:
A person drops a cannon ball off the side of a ship. On the ship, the cannon ball
appears to fall straight down, due to the force of gravity. On shore the cannon
ball falls down due to gravity PLUS has a constant horizontal speed, which is
equal to the speed of the ship. Both reference frames are inertial. Only a constant
velocity makes them different. They move relative to each other. On board the
ship, the shore appears to move aft. On the shore, the ship appears to move in the
opposite direction.
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