1
PHYS 342
Fall Semester 2011
Homework No. 7
Due: December 7, 2011
1.
A reoccurring theme in the physics of relativity
is the transformation of results between
different coordinate systems.
One important
nonrelativistic
transformation involves two
coordinate systems that are rotated one with
respect to the other. Suppose there are two co
ordinate systems (x,y,z) and (x’,y’,z’) as shown
to the right. The primed coordinate system is
rotated through an angle +
as shown. The co
ordinates of a point P (x,y,z) are related to the coordinates of the
same point P (x’,y’,z’) when measured in the rotated coordinate system by
a)
Suppose there are two vectors
ˆˆ
ˆ
ˆ
61
0 9
3
3
A
ij
k
a
n
d
B
i
j
k
in the unprimed
coordinate system. What are these vectors when measured in the primed coordinate
system if the rotation angle
=35
o
?
b)
Evaluate the vector products
ABandA B
in both the primed and unprimed co
ordinate systems? Are either of these two vector operations invariant under
coordinate transformation?
P
x
x’
y
y’
z
z’
'c
o
s
s
i
n
0
's
i
n
c
o
s
0
'0
0
1
x
x
y
y
zz
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c) What is the length of the vector (
A A
) in both the primed and unprimed co
ordinate systems.
Is the length of a vector invariant under rotation of the coordinate
axes?
2.
A spacecraft travels in a straight line at a speed of 0.50c. An astronaut holds a
meter stick parallel to the direction of travel.
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 Fall '08
 Staff
 Energy, Kinetic Energy, Mass, Momentum, Work, Special Relativity, relativistic energy formula

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