Happyphysics.com Physics Lecture Resources Prof. Mineesh Gulati Head-Physics Wing Happy Model Hr. Sec. School, Udhampur, J&K Website: happyphysics.com

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Prof. Mineesh GulatiHead-Physics Wing

Happy Model Hr. Sec. School, Udhampur, J&K

Website: happyphysics.com

Ch 37 Relativity

© 2005 Pearson Education

37.1 Invariance of Physical Laws37.1 Invariance of Physical Laws


Same emf induced

Einstein’s PostulateEinstein’s Postulate

First PostulateFirst Postulate: The laws of physics are : The laws of physics are the same in every inertial frame of the same in every inertial frame of reference.reference.

Second PostulateSecond Postulate: The speed of light in : The speed of light in vacuum is the same in all inertial vacuum is the same in all inertial frames of reference and is independent frames of reference and is independent of the motion of the source.of the motion of the source.




Galilean coordinate transformation

Galilean coordinate Galilean coordinate transformationtransformation

' ' 'x x ut y y z z

Galilean velocity Galilean velocity transformationtransformation

'x xv v u


37.2 relativity of Simultaneity37.2 relativity of Simultaneity



Whether or not two events at different x-axis locations are simultaneous depends on the state of motion of the observer

37.3 Relativity of Time Intervals


At rest: ∆t0=2d/c

During time ∆tDuring time ∆t

2 2

22

2 2

0

0

2

2

( )2

2 2

2

2

2 2

1

u tl d

l u tt d

c c

c t u ttc

tt

uc


time dilation

22

0

1 cu

tt

221

1

cu

0tt



Example 37.1High-energy subatomic particles coming from spHigh-energy subatomic particles coming from space interact with atoms in the earth’s upper atmace interact with atoms in the earth’s upper atmosphere, producing unstable particles called muoosphere, producing unstable particles called muons. A muon decays with a mean lifetime of 2.2*10ns. A muon decays with a mean lifetime of 2.2*10--

66s as measured in a frame of reference in which it s as measured in a frame of reference in which it is at rest. If a muon is moving at 0.99c relative to tis at rest. If a muon is moving at 0.99c relative to the earth, what will you measure its mea lifetime the earth, what will you measure its mea lifetime to be?o be?

ANS:ANS:


60

2 2 2

6

2.2 10

1 / 1 (0.99)

15.6 10

t st

u c

s

37.4 Relativity of Length

0

2

2

0 1l

c

ull

length contraction


Example 37.4

A spaceship flies past earth at a speed A spaceship flies past earth at a speed of 0.99c. A crew member on board the of 0.99c. A crew member on board the spaceship measures its length, obtaining spaceship measures its length, obtaining the value 400m. What length do the value 400m. What length do observers measure on earth?observers measure on earth?

ANS:ANS: 2

0 2

2

1

(400 ) 1 (0.99)

56.4

ul l

c

m

m


37.5 The Lorentz Transformations


)(1

2

22

2

cuxtcu

cuxtt

zz

yy

utxcu

utxx

)(1 22

Lorentz coordinate transformation

21 cuv

uvv

x

xx

Lorentz velocity transformation

21 cvu

uvv

x

xx


37.6 the Doppler Effect for Electromagnetic Waves

Doppler effect, electromagnetic waves


0fuc

ucf

relativistic momentum

221 cv

m

vp

vp

mγ

37.7 Relativistic Momentum


37.8 Relativistic Work and Energy


relativistic kinetic energy

22

22

2

)1(1

mcmccv

mcK

total energy, rest energy, and momentum

2

22

22

1mc

cv

mcmcKE

2222 )()( pcmcE


37.9 Newtonian Mechanics and Relativity



All of the fundamental laws of physics have the same form in all inertial frames of reference. The speed of light in vacuum is

the same in all inertial frames and is independent of the motion of the source. Simultaneity is not an absolute concept; events that are simultaneous in one frame are not necessarily simultaneous in a second frame moving relative to the first.

If two events occur at the same space point in a particular frame of reference, the time interval ∆t0 between the events as measured in that frame is called a proper time interval. If this frame moves with constant velocity u relative to a second frame, the time interval ∆t

between the events as observed in the second frame is longer than ∆t0 . This effect is called time dilation. (Examples 37.1 through

37.3)


If two points are at rest in a particular frame of reference, the distance l0 between the points as measured in that frame is

called a proper length. If this frame moves with constant velocity u relative to a second frame and the distances are measured parallel to the motion, the distance l between the

points as measured in the second frame is shorter than l0 . This effect is called length contraction. (See Examples 37.4 through

37.6)


The Lorentz coordinate transformation relates the coordinate and time of an event in an inertial frame S to the coordinates and time of the same event as observed in a second inertial frame S’

moving at velocity u relative to the first. For one-dimensional motion, a particle’s velocities vx in S and v’x in S’ are related by the Lorentz velocity transformation. (See Examples 37.7 and 37.8)



The Doppler effect is the frequency shift in light from a source due to the relative motion of source and observer. For a source moving toward the observer with speed u, Eq.(37.25) gives the received frequency f in terms of the emitted frequency f0.(See

Example 37.9)

For a particle of rest mass m moving with velocity , the relativistic momentum is given by Eq. (37.27) or (37.31) and the relativistic kinetic energy K is given by Eq. (37.36). The total energy E is the sum of the kinetic energy and the rest energy mc2 . The total energy can also be expressed in terms of the magnitude of momentum p and rest mass m. (See Examples 37.10 through 37.12)


v

p


The special theory of relativity is a generalization of Newtonian mechanics.

All the principles of Newtonian mechanics are present as limiting cases when all the speeds are

small compared to c. Further generalization to

include noninertial frames of reference and their

relation to gravitational fields leads to the general

theory of relativity.

ENDEND

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Happyphysics.com Physics Lecture Resources Prof. Mineesh Gulati Head-Physics Wing Happy Model Hr. Sec. School, Udhampur, J&K Website: happyphysics.com