College Physics for AP® Courses

# Glossary

the method of adding velocities when $v<; velocities add like regular numbers in one-dimensional motion: $u=v+u′u=v+u′$, where $vv$ is the velocity between two observers, $uu$ is the velocity of an object relative to one observer, and $u′u′$ is the velocity relative to the other observer
first postulate of special relativity
the idea that the laws of physics are the same and can be stated in their simplest form in all inertial frames of reference
inertial frame of reference
a reference frame in which a body at rest remains at rest and a body in motion moves at a constant speed in a straight line unless acted on by an outside force
length contraction
$LL size 12{L} {}$, the shortening of the measured length of an object moving relative to the observer’s frame: $L=L01−v2c2=L0γL=L01−v2c2=L0γ size 12{ ital "L=L" rSub { size 8{0} } sqrt {1 - { {v rSup { size 8{2} } } over {c rSup { size 8{2} } } } } = { {L rSub { size 8{0} } } over {γ} } } {}$
Michelson-Morley experiment
an investigation performed in 1887 that proved that the speed of light in a vacuum is the same in all frames of reference from which it is viewed
proper length
$L0L0 size 12{L rSub { size 8{0} } } {}$; the distance between two points measured by an observer who is at rest relative to both of the points; Earth-bound observers measure proper length when measuring the distance between two points that are stationary relative to the Earth
proper time
$Δt0Δt0$. the time measured by an observer at rest relative to the event being observed: $Δt=Δt01−v2c2=γΔt0Δt=Δt01−v2c2=γΔt0$, where $γ=11−v2c2γ=11−v2c2$
relativistic Doppler effects
a change in wavelength of radiation that is moving relative to the observer; the wavelength of the radiation is longer (called a red shift) than that emitted by the source when the source moves away from the observer and shorter (called a blue shift) when the source moves toward the observer; the shifted wavelength is described by the equation
$λ obs =λ s 1 + u c 1 − u c λ obs =λ s 1 + u c 1 − u c$
where $λobsλobs$ is the observed wavelength, $λsλs$ is the source wavelength, and $uu$ is the velocity of the source to the observer
relativistic kinetic energy
the kinetic energy of an object moving at relativistic speeds: $KErel=γ−1mc2KErel=γ−1mc2 size 12{"KE" rSub { size 8{"rel"} } = left (γ - 1 right ) ital "mc" rSup { size 8{2} } } {}$, where $γ=11−v2c2γ=11−v2c2$
relativistic momentum
$pp size 12{p} {}$, the momentum of an object moving at relativistic velocity; $p=γmup=γmu size 12{p= ital "γmu"} {}$, where $mm size 12{m} {}$ is the rest mass of the object, $uu size 12{u} {}$ is its velocity relative to an observer, and the relativistic factor $γ=11−u2c2γ=11−u2c2 size 12{γ= { {1} over { sqrt {1 - { {u rSup { size 8{2} } } over {c rSup { size 8{2} } } } } } } } {}$
the method of adding velocities of an object moving at a relativistic speed: $u=v+u′1+vu′c2u=v+u′1+vu′c2$, where $vv size 12{v} {}$ is the relative velocity between two observers, $uu size 12{u} {}$ is the velocity of an object relative to one observer, and $u′u′ size 12{u rSup { size 8{'} } } {}$ is the velocity relative to the other observer
relativity
the study of how different observers measure the same event
rest energy
the energy stored in an object at rest: $E0=mc2E0=mc2$
rest mass
the mass of an object as measured by a person at rest relative to the object
second postulate of special relativity
the idea that the speed of light $cc size 12{c} {}$ is a constant, independent of the source
special relativity
the theory that, in an inertial frame of reference, the motion of an object is relative to the frame from which it is viewed or measured
time dilation
the phenomenon of time passing slower to an observer who is moving relative to another observer
total energy
defined as $E=γmc2E=γmc2$, where $γ=11−v2c2γ=11−v2c2$
this asks why a twin traveling at a relativistic speed away and then back towards the Earth ages less than the Earth-bound twin. The premise to the paradox is faulty because the traveling twin is accelerating, and special relativity does not apply to accelerating frames of reference
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