Physics 2514
Lecture 18
P. Gutierrez
Department of Physics & Astronomy
University of Oklahoma
Physics 2514 – p. 1/14
Goals
Discuss relative motion and reference frames quantitatively.
Physics 2514 – p. 2/14
Newton’s First Law of Motion
Newton’s first law defines what we mean by a force, “it is what
causes an object to change its velocity”. It also specifies under
what conditions Newton’s laws of motion hold.
Newton’s laws hold only in inertial frames of reference
(Reference frames that move at constant velocity relative to the
most distance stars).
A reference frame is a coordinate system used to define the
position of objects. It can be stationary, moving with constant
velocity or accelerated relative to the most distance stars.
Physics 2514 – p. 3/14
Reference Frame
A reference frame is a coordinate system that can be attached
to an object (system) and move with it;
y0
y
v 0 (t)
PSfrag replacements
x0
x
v(t)
If v(t) or v 0 (t) are constant, then the unprimed or primed frame
is an inertial reference frame. Motion relative to a fixed inertial
reference frame.
Physics 2514 – p. 4/14
Relative Position
Position and motion are relative;
Consider two observers moving relative to each other;
Which frame is moving and which
is stationary is a matter of who
the observer is
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Reference Frame
We will impose the following conditions on reference frames
in this course:
The frames are oriented the same, with x and x0 axis
parallel, the same holds for the y and y 0 axis;
The origin’s of frame S and S 0 coincide at t = 0;
All motion is assumed in the x-y plane;
The relative velocity V is constant.
The first 3 statements are a matter of how we define our
coordinate system. The last item specifies we are working with
inertial frames of reference.
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Relative Position
Inertial Frames
Position in unprimed frame
relative to primed
~
~
~r = ~r0 + R(t)
= ~r0 + Vt
In component form this
becomes
x = x 0 + Vx t
y = y 0 + Vy t
Physics 2514 – p. 7/14
Relative Velocity
Velocity in unprimed frame
relative to primed
~
d~r0 dR
d~r
=
+
dt
dt dt
⇒
~
~v = ~v0 +V
In component form this
becomes
vx = vx0 + Vx
vy = vy0 + Vy
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Clicker
A plane traveling horizontally to the right at 100 m/s flies past a
helicopter that is going straight up at 20 m/s. From the
helicopters perspective, the plane’s direction and speed are:
1. Right and up, 100 m/s;
2. Right and up, more than 100 m/s;
3. Right and down less, than 100 m/s;
4. Right and down, 100 m/s;
5. Right and down, more than 100 m/s
Physics 2514 – p. 9/14
Principle of Relativity
In what frame do Newton’s laws hold?
Consider two frames S and S 0 moving relative to each
other;
Assume that an object is seen to accelerate in frame S 0
Frame S sees
~
d~v0 dV
d~v0
d~v
=
+
=
dt
dt
dt
dt
~ is constant, both frames see the same acceleration
if V
and measure the same force ~a = ~a0 (Newton’s second
law holds)
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Principle of Relativity
Assume that an object is seen to move at a constant
velocity in frame S 0
Frame S sees
~
~
d~v0 dV
dV
d~v
=
+
=
=0
dt
dt
dt
dt
~ is constant, Newton’s first law holds in both frames.
if V
Principle of Relativity Newton’s laws of motion hold in all inertial
frames.
Physics 2514 – p. 11/14
Example
Mike throws a ball at a speed of 22 m/s with an angle of 63◦ relative to
the horizontal. Nancy drives past Mike at 30 m/s at the instant he
releases the ball. What is the ball’s initial speed and angle in Nancy’s
g replacements
reference frame.
y
y0
S is Mike’s frame (rest frame)
S 0 is Nancy’s frame (moving frame)
S0
S
~
Will use ~
v=~
v0 + V
Known
~
V
~
v = v cos θ î + v sin θ ĵ = 10.0 î + 19.6 ĵ
~ = V î = 30 î
V
~
v
θ
Unknown
x0
x
~ = −20. î + 19.6 ĵ
~
v−V
v0 = ~
~
v0 = v 0 cos θ 0 î + v 0 sin θ 0 ĵ
⇒
8
„
«
19.6
>
>
= −44.4◦
< θ0 = tan−1
−20
q
>
>
: v 0 = (−20)2 + (19.6)2 = 28 m/s
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Clicker
Nancy is riding on a train that is traveling at 30 m/s relative to the
train station. If she is walking at 1 m/s relative to the train in a
direction opposite its motion, what is her speed relative to Mike
who is sitting in the train station?
A) 30 m/s
B) 29 m/s
C) 31 m/s
D) 60 m/s
E) where’s Waldo?
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Assignment
Start reading Chapter 7
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