Frames of Reference and Relativity
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11.1 – Frames of Reference
and Relativity
Inertial Frame of Reference (IFOR)
•
a frame of reference in which
the law of inertia holds
•
The FOR must be at a
constant velocity (not speed)
or at rest
•
In both, net force = 0N
a) Pick-up at const vel b) Earth is stationary
Non-Inertial Frame of
Reference (NIFOR)
•
a frame of reference that
does not obey the law of
inertia
•
the reference involves
acceleration. (A Nonzero
Net Force)
•
From inside the accelerating car, the ball
appears to move without a force acting on it
(Breaks Newt’s 2
nd
Law)
Guidelines for IFOR’s
1. An inertial frame of reference
is one which an object has no
net force acting on it; and it is
at rest or moving at a constant
velocity.
Guidelines for IFOR’s
2. The laws of Newtonian
mechanics are only valid in an
inertial frame of reference.
Guidelines for IFOR’s
3. The laws of Newtonian
mechanics apply equally in all
inertial frames of reference.
•
In an IFOR, you cannot tell
if you are moving or not
•
Your FOR could be moving
at a constant vel. and you
would never know
Special Theory of Relativity
•
What would happen if you are moving
at the speed of light in a car and then
you turn your headlights on?
•
This is the type of thought experiment
Einstein performed to conceptualize
movement at very high speeds (closer
to speed of light)
Special Theory of Relativity
1.
The relativity
principle
:
all the laws of physics
are valid in
all inertial frames of
reference.
Special Theory of Relativity
2.
The consistency
of the speed of light
:
light travels through empty space
with a speed of c = 3.00 X 10
8
m/s relative to all inertial frames
of reference.
•
Einstein defined light as the
universal speed limit
Simultaneity
•
The occurrence of two or more
events at the same time is a relative
concept
•
Two events that are simultaneous in
one FOR are in general not
simultaneous in a second FOR
moving with respect to the first
•
Simultaneity is not an absolute
concept
11.2 – Relativity of Time,
Length and Momentum
•
Time dilation
: the effect of
time occurring slower in one
system compared to another
system.
•
Note: As objects move faster
relative to the Earth, time
slows down.
•
Note: Dilation means
widening, thus time dilation
means widening time.
•
Proper time occurs when an
observer remains in one
system of time.
Einstein’s Proof for Time Dilation
•
The light clock
•
t
m
=
t
s
/[1-(v
2
/c
2
)]
0.5
where
t
m
= time for moving observer
t
s
= time for stationary observer
v = speed of moving observer
( in m/s)
c = speed of light
( 3.00 X 10
8
m/s)
Note: Use the person in the ship as a
reference.
•
Example # 1:
A person travels for 3.0 years
at the speed 0.70c relative to a
physics student on Earth.
Calculate the time that has
passed for the student.
•
Solution
t
m
=
t
s
/[(1-(v
2
/c
2
)]
0.5
t
m
= (3.0 years)/[1-
(0.70c)
2
/c
2
]
0.5
= 4.2 years
•
The time for the moving
observer is 4.2 years.
The Twin Paradox
•
Einstein had a
thought experiment
involving two twins,
in which one went
to a star at a speed
near the speed of
light and then came
back to Earth.
Which twin would be older?
The one on Earth?
Or the one on the spacecraft?
•
Proper Length
: the length of
an object at rest
•
Length Contraction
: the
shortening of distances in a
system as seen by an observer
in motion relative to that
system.
•
Length contraction only
occurs in the direction of
motion
•
L
m
= L
s
(1- v
2
/c
2
)
0.5
Where
L
m
= length for moving observer
L
s
= length for stationary
observer
v = speed of moving observer
( in m/s)
c = speed of light
( 3.00 X 10
8
m/s)
Example # 2
: Calculate
the proper length of an
object that has a L
m
=
45 m when it is moving
at 0.60c.
Solution
L
m
= L
s
(1- v
2
/c
2
)
0.5
L
s
= L
m
/(1- v
2
/c
2
)
0.5
= (45 m) /[1- (0.60c)
2
/c
2
]
0.5
= 56 m
•
The proper length is 56 m.
Example # 3
If two spaceships, 40m long,
are travelling towards each
other at 0.20c and 0.30c,
what will each pilot see as
the length of the other ship?
Relativistic Momentum
:
the momentum of an
object travelling at a
speed at 0.10c or
greater.
p = mv/(1- v
2
/c
2
)
0.5
where
p = magnitude of relativistic
momentum (in kg•m/s)
m = rest mass (in kg)
v = speed of an object (in m/s)
Example # 3
:
Calculate the magnitude of
relativistic momentum of an
object that has a mass of 600
kg at a speed of 0.80c.
Solution
p = mv/(1- v
2
/c
2
)
0.5
p =
(600kg)(0.80)(
3.00X10
8
ms)
[1-(0.80c)
2
/c
2
]
0.5
p = 2.4 X 10
11
kg•m/s
The magnitude of relativistic
momentum is 2.4 X 10
11
kg•m/s.
11.2 Practice Questions
•
Page 573 Questions 1-3
•
Page 576 Questions 5-9
•
Page 578 Questions 10,11
•
Page 579 Questions 1- 5
Explore the concept of frames of reference in physics, distinguishing between inertial and non-inertial frames. Learn about the laws of Newtonian mechanics, guidelines for inertial frames of reference, and delve into the intriguing realm of the Special Theory of Relativity with engaging visual aids and thought experiments.
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Presentation Transcript
11.1 Frames of Reference and Relativity
Inertial Frame of Reference (IFOR) a frame of reference in which the law of inertia holds The FOR must be at a constant velocity (not speed) or at rest In both, net force = 0N
a) Pick-up at const vel b) Earth is stationary
Non-Inertial Frame of Reference (NIFOR) a frame of reference that does not obey the law of inertia the reference involves acceleration. (A Nonzero Net Force)
From inside the accelerating car, the ball appears to move without a force acting on it (Breaks Newt s 2ndLaw)
Guidelines for IFORs 1. An inertial frame of reference is one which an object has no net force acting on it; and it is at rest or moving at a constant velocity.
Guidelines for IFORs 2. The laws of Newtonian mechanics are only valid in an inertial frame of reference.
Guidelines for IFORs 3. The laws of Newtonian mechanics apply equally in all inertial frames of reference.
In an IFOR, you cannot tell if you are moving or not Your FOR could be moving at a constant vel. and you would never know
Special Theory of Relativity What would happen if you are moving at the speed of light in a car and then you turn your headlights on? This is the type of thought experiment Einstein performed to conceptualize movement at very high speeds (closer to speed of light)
Special Theory of Relativity 1. The relativity principle: all the laws of physics are valid in all inertial frames of reference.
Special Theory of Relativity 2. The consistency of the speed of light: light travels through empty space with a speed of c = 3.00 X 108 m/s relative to all inertial frames of reference. Einstein defined light as the universal speed limit
Simultaneity The occurrence of two or more events at the same time is a relative concept Two events that are simultaneous in one FOR are in general not simultaneous in a second FOR moving with respect to the first Simultaneity is not an absolute concept
11.2 Relativity of Time, Length and Momentum
Time dilation: the effect of time occurring slower in one system compared to another system. Note: As objects move faster relative to the Earth, time slows down.
Note: Dilation means widening, thus time dilation means widening time. Proper time occurs when an observer remains in one system of time.
Einsteins Proof for Time Dilation The light clock
tm= ts/[1-(v2/c2)]0.5 where tm= time for moving observer ts= time for stationary observer v = speed of moving observer ( in m/s) c = speed of light ( 3.00 X 108m/s)
Note: Use the person in the ship as a reference. Example # 1: A person travels for 3.0 years at the speed 0.70c relative to a physics student on Earth. Calculate the time that has passed for the student.
Solution tm= ts/[(1-(v2/c2)]0.5 tm= (3.0 years)/[1- (0.70c)2/c2] 0.5 = 4.2 years The time for the moving observer is 4.2 years.
The Twin Paradox Einstein had a thought experiment involving two twins, in which one went to a star at a speed near the speed of light and then came back to Earth.
Proper Length: the length of an object at rest Length Contraction: the shortening of distances in a system as seen by an observer in motion relative to that system.
Length contraction only occurs in the direction of motion
Lm= Ls(1- v2/c2)0.5 Where Lm= length for moving observer Ls= length for stationary observer v = speed of moving observer ( in m/s) c = speed of light ( 3.00 X 108m/s)
Example # 2: Calculate the proper length of an object that has a Lm= 45 m when it is moving at 0.60c.
Solution Lm= Ls(1- v2/c2)0.5 Ls= Lm/(1- v2/c2)0.5 = (45 m) /[1- (0.60c)2/c2]0.5 = 56 m The proper length is 56 m.
Example # 3 If two spaceships, 40m long, are travelling towards each other at 0.20c and 0.30c, what will each pilot see as the length of the other ship?
Relativistic Momentum: the momentum of an object travelling at a speed at 0.10c or greater.
p = mv/(1- v2/c2)0.5 where p = magnitude of relativistic momentum (in kg m/s) m = rest mass (in kg) v = speed of an object (in m/s)
Example # 3: Calculate the magnitude of relativistic momentum of an object that has a mass of 600 kg at a speed of 0.80c.
Solution p = mv/(1- v2/c2)0.5 p = (600kg)(0.80)(3.00X108ms) [1-(0.80c)2/c2]0.5 p = 2.4 X 1011kg m/s The magnitude of relativistic momentum is 2.4 X 1011kg m/s.
11.2 Practice Questions Page 573 Questions 1-3 Page 576 Questions 5-9 Page 578 Questions 10,11 Page 579 Questions 1- 5
