PHYS 111 Chapter Notes - Chapter 1: Lorentz Transformation, Length Contraction, Invariant Mass

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1 Aug 2016
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Physics (111) Concept Understanding of Relativity:
Try the questions with red answers covered up.
What are the two postulates of special relativity?
The laws of physics must be the same in all inertial reference frames.
The speed of light in vacuum has the same value, c =3.00 10^8 m/s, in all
inertial frames, regardless of the velocity of the observer or the velocity of
the source emitting the light.
Explain the consequences of special relativity.
Events that are measured to be simultaneous for one observer are not
necessarily measured to be simultaneous for another observer who is in
motion relative to the first.
Clocks in motion relative to an observer are measured to run slower by a
factor γ =(1 – v^2/c^2)^-1/2. This phenomenon is known as time dilation.
The length of objects in motion are measured to be contracted in the
direction of motion by a factor 1/=(1 – v^2/c^2)^1/2. This phenomenon is
known as length contraction.
To satisfy the postulates of special relativity, the Galilean transformation equations
must be replaced by the Lorentz transformation equations where γ =(1 –
v^2/c^2)^-1/2 and the S’ frame moves in the x direction relative to the S frame.
The relativistic form of the velocity transformation equation is:
where u
x is the speed of an object as measured in the S frame and u
x’ is its speed
measured in the S’ frame.
The relativistic expression for the linear momentum of a particle moving
with a velocity u is:
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