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Inertial and Non-Inertial Frames of Reference

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Inertial and Non-Inertial Frames of Reference SPH4U Grade 12 Physics Unit 3 Inertial and Non-Inertial Reference Frames Recall: Newton s first law of motion (law ... – PowerPoint PPT presentation

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Title: Inertial and Non-Inertial Frames of Reference


1
Inertial and Non-Inertial Frames of Reference
  • SPH4U Grade 12 Physics
  • Unit 3

2
Inertial and Non-Inertial Reference Frames
  • Recall Newtons 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
  • Weve 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 balls
    velocity than a person standing outside the bus
    would measure the balls velocity.

4
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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
  • Lets 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 Newtons 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 Newtons first law?

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 its 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 its forward velocity with no net
    force.

16
Inertial and Non-Inertial Reference Frames
  • To explain the balls 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 balls 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 balls 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 havent 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.

25
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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?
28
Homework
  • Read Sections 3.1. Supplement info from the text
    into your note.
  • What is an accelerometer? Explain how an
    accelerometer works.
  • Answer the following questions
  • Pg. 113 2, 4, 6, 7
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