This document discusses inertial and non-inertial reference frames. It explains that an inertial reference frame is one in which Newton's laws of motion are valid, while a non-inertial frame is one in which they are not valid. When observing motion from a non-inertial frame, such as an accelerating bus, fictitious forces must be introduced to explain the observed motion. The document uses examples of balls on moving trains and subways to illustrate inertial and non-inertial frames. It concludes by relating non-inertial frames to the feeling of weightlessness on roller coasters during free fall.

1. Inertial and Non-
Inertial Frames of
Reference
BY AARTI PANWAR
SUBMITTED TO GYANRAO DHOTE

2. Inertial and Non-Inertial Reference
Frames
 Recall: Newton’s first law of motion (law of
inertia):
An object at rest stays at rest and an object in
motion stays in motion with the same speed
and in the same direction unless acted upon by
an unbalanced force.

3. Inertial and Non-Inertial Reference
Frames
 We’ve already talked about frames of reference
in this course when we talked about relative
velocity. You know that a person sitting on a
bus watching a ball roll across the ground will
have a very different measurement of the ball’s
velocity than a person standing outside the bus
would measure the ball’s velocity.

4. That ball
is moving
at 5km/h
That ball is
moving at
15 km/h
Bus moves at 20km/h

5. Inertial and Non-Inertial Reference
Frames
 The person inside the bus and the person
outside the bus are measuring from different
frames of reference.

6. Inertial and Non-Inertial Reference
Frames
 Let’s change things a little…
 Imagine that you are travelling on the bus with a
ball beside you sitting on the floor. The bus is
moving forward at a constant velocity of 20km/h.
Bus moves at 20km/h

7. Inertial and Non-Inertial Reference
Frames
 The ball on the floor does not move, which is as
it should be because there is no net force acting
on it and Newton’s first law says that it should
stay resting unless acted on by some force.
The ball is
still. All is
well.
Bus moves at 20km/h

8. Inertial and Non-Inertial Reference
Frames
 Suddenly, the bus starts to decelerate…
Bus is slowing down

9. Inertial and Non-Inertial Reference
Frames
 Suddenly, the bus starts to decelerate…
… and The ball starts to accelerate toward the
front of the bus...
Wait…
what
the…
Bus is slowing down

10. Inertial and Non-Inertial Reference
Frames
 Since there is no net force acting on this ball (no
one pushed it) what is going on? Does this
violate Newton’s first law?
The laws of
physics are
deteriorating!
Bus is slowing down

11. Inertial and Non-Inertial Reference
Frames
 The laws of physics seem to momentarily break
down for you sitting on the bus. In reality, what
has happened is that your frame of reference
has been compromised.

12. Inertial and Non-Inertial Reference
Frames
 An inertial frame of reference is a frame of
reference in which the law of inertia and other
physics laws are valid. Any frame moving at a
constant velocity relative to another frame is also
an inertial frame of reference.

13. Inertial and Non-Inertial Reference
Frames
 When the breaks are applied to the bus, the bus
undergoes a negative acceleration. At this
moment, it becomes a non-inertial frame of
reference.
 A non-inertial frame of reference is a reference
frame in which the law of inertia does not
hold.

14. Inertial and Non-Inertial Reference
Frames
 Although the ball accelerates toward the front of
the bus, there is no net force causing the
acceleration.
 But if you are sitting on the bus, you observe the
ball accelerating forward. That would imply to
you as you sit on the bus that there is a net
force forward on the ball.
 The reason there appears to be a net force on
the ball is that you are observing the motion of
the ball in the non-inertial reference frame.

15. Inertial and Non-Inertial Reference
Frames
 If you were observing the motion from the road
(which is an inertial frame of reference) the ball
just continues to move forward at the speed it
was already going, and it’s motion is easily
explained by the law of inertia.
 To an observer in the inertial frame of reference
(the ground) the bus experiences a net force
causing it to decelerate. The ball just continues
it’s forward velocity with no net force.

16. Inertial and Non-Inertial Reference
Frames
 To explain the ball’s motion if you are sitting on
the bus, you need to invent a force that acts on
the ball toward the front of the bus. This is
called the fictitious force. It is an invented
force that we can use to explain the observed
motion in the accelerated frame of reference.

17. Example 1
 You are on a train which is initially travelling at
12m/s [E]. You gently place a tennis ball
beside your seat.
a) What happens to the tennis ball’s motion?
b) Draw an FBD of the ball in the frame of reference
of the ground outside the train, and the frame of
reference of the train
c) The train starts to accelerate east. Draw a new
FBD of the ball in both frames of reference.

18. Example 1
 You are on a train which is initially travelling at 12m/s
[E]. You gently place a tennis ball beside your seat.

a) What happens to the tennis ball’s motion?
b) Draw an FBD of the ball in the frame of
reference of the ground outside the train, and the
frame of reference of the train
c) The train starts to accelerate east. Draw a new
FBD of the ball in both frames of reference.

19. Example 2
 A rubber stopper of mass 25g is suspended by
string from the handrail of a subway car
travelling directly westward. As the subway
train nears a station, it begins to slow down,
causing the stopper and string to hang at an
angle of 13º from the vertical.
a) What is the acceleration of the train?
b) Determine the magnitude of the tension in the string.

20. Example 2
A rubber stopper of mass 25g is suspended by string
from the handrail of a subway car travelling directly
westward. As the subway train nears a station, it
begins to slow down, causing the stopper and string to
hang at an angle of 13º from the vertical.
a) What is the acceleration of the train?
Thus, the acceleration of
the train is 2.3 m/s2
[E]

21. Example 2
A rubber stopper of mass 25g is suspended by string
from the handrail of a subway car travelling directly
westward. As the subway train nears a station, it
begins to slow down, causing the stopper and string to
hang at an angle of 13º from the vertical.
b) Determine the magnitude of the tension in the string.
Thus, the magnitude of the tension
in the string is 0.25 N.

22. What does this have to do with
Roller coasters?
 One of the things that makes roller coasters fun
is the feeling of weightlessness you have when
you are going down a big hill.
 That feeling of weightlessness occurs because
your apparent weight as you are in free fall down
the hill is zero.
 Apparent weight is the magnitude of the normal
force acting on an object in a non-inertial frame
of reference.

23. What does this have to do with
Roller coasters?
 When we are standing up
on level ground, we
experience a normal force
up. This is the force of the
ground against our feet.
 If you stand on a bathroom
scale, the normal force up
is equal to your weight on
the scale (mg)

24. What does this have to do with
Roller coasters?
 If you were to put that scale in an elevator, which
is accelerating downward, the normal force will
decrease, and your weight reading on the scale
will appear to be less.
 You haven’t actually lost any mass, but in the
accelerated reference frame, the normal force
decreases because you and the elevator are
accelerating, and therefore your weight will read
as less.

26. What does this have to do with
Roller coasters?
 Your new weight in this accelerated, non-inertial
reference frame is called the ‘apparent weight’.
 On a roller coaster, when you are in free fall
down a large hill, the acceleration of the ride is
equal to g (9.81 m/s2
) and the normal force
between you and your seat becomes zero. This
makes your apparent weight zero as you go
down the hill, and is the reason you feel
‘weightless’: you no longer have the normal
force of the seat pressing up against you.

27. What does this have to do with
Roller coasters?