PHYS2004 (1
st
Term 10/11)
1
Assignment 3
Section A (Compulsory – due on 14/10/2010 Thu (before 5:00 pm))
1.
A point
P
moves on the curve
exp
cot
ra
,
in such a way that its radius vector
OP
rotates about the origin with the constant
angular velocity
.
Find the radial and transverse components of its velocity, and
show that the resultant velocity makes a constant angle with the radius vector. (it is an
equiangular spiral
)
[50 marks]
2.
The velocity of a particle at time
t
is given by
ˆ
ˆ
ˆ
sin 2
2cos2
vt
i
t
j
t
k
.
Find its position as a function of time, given that at time
0
t
it was located at the
point
3, 1,
3
.
Show the velocity and acceleration vectors can never be orthogonal
if
3
t
.
[50 marks]
Section B (Optional Questions for STOT groups – please submit in STOT group sessions)
3.
A
33
matrix
A
has elements
ij
i
j
ilj
l
An
n
n
,
where
i
n
are the components of a unit vector in
3
.
Show that the elements of the
matrix
2
A
are given by
2
2
ij
i
j
ij
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 Spring '10
 DrKwong
 Derivative, Trigraph, Parametric equation, radius vector OP

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