1. Physics: Principles with Applications, 6th edition
Lecture PowerPoints
Chapter 2
Physics: Principles with Applications, 6th edition
Giancoli
© 2005 Pearson Prentice Hall
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2. Reference Frames and Einstein’s Special Theory of Relativity
Inertial reference frame – reference frame in which Newton’s First Law of Motion holds (every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it).

3. Reference Frames and Einstein’s Special Theory of Relativity
First Postulate: The laws of physics have the same form in all inertial reference frames (relativity principle)
Second Postulate: Light propagates through empty space with a definite speed of c independent of the source or observer. (constancy of the speed of light). [The speed of light is the same in ALL inertial reference frames]

4. Reference Frames and Einstein’s Special Theory of Relativity
Note that the effects of the Special Theory of Relativity are too small to be measured unless an object is travelling at some large fraction of the speed of light, c, or 2.99 x 1010 m/s (these are referred to as relativistic velocities).
So the equations that show the consequences of the Special Theory of Relativity reduce to the classical equations at normal velocities

5. Reference Frames and Einstein’s Special Theory of Relativity
Consequences of the Special Theory of Relativity
Source:

6. Reference Frames and Einstein’s Special Theory of Relativity
Consequences of the Special Theory of Relativity
Time dilation – clocks moving relative to an observer are measured by that observer to run more slowly (as compared to clocks at rest)
Example: Twin 20 year old astronauts. One travels at very high speed to a distant star and returns. The other remains on Earth. According to the Earth twin, only 1 year might pass for the traveler, while 20 years would have passed for the earthbound twin, who would now be 40 compared to her twin’s age of 21 years.

7. Reference Frames and Einstein’s Special Theory of Relativity
Consequences of the Special Theory of Relativity
Length contraction – objects moving relative to an observer are measured by that observer to be shorter in the direction of travel (as compared to objects of the same length at rest)
Example: A painting hangs on the wall of a spaceship passing Earth at 0.9 c. It is 1.50 m wide by 1.00 m tall.
As seen by an observer on Earth, the painting would appear to be only 0.65 m wide
Length contraction

8. Reference Frames and Einstein’s Special Theory of Relativity
Consequences of the Special Theory of Relativity
Energy: Particles that are moving have kinetic enegy. Even when a particle is at rest, it has energy. The formula for determining that energy is E = mc2.

9. Reference Frames and Einstein’s Special Theory of Relativity
Consequences of the Special Theory of Relativity
Momentum: masses moving relative to an observer are measured by that observer to have more mass (as compared to objects at rest).
Example: the mass of an electron in an accelerator used for cancer therapy has a velocity of 0.98 c. Its momentum would be 5.0 times the momentum of an electron at rest.

10. Reference Frames and Einstein’s Special Theory of Relativity
Lorentz Transformation
The Lorentz Transformation shows the changes that occur classical kinematics due to the Special Theory of Relativity

11. Reference Frames and Einstein’s Special Theory of Relativity
Summary
All inertial reference frames obey the same laws of physics
The speed of light in empty space, c, does not change when the reference frame changes
No object can move faster than the speed of light
At everyday velocities, the consequences of special relativity are too small to be noticed or measured
At relativistic velocities, an observer will see that clocks, lengths in the direction of travel, momentum and energy will be different than those at rest with respect to the observer.
Even at rest, objects with mass have energy equal to their mass x c2