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Mathematics
Problem
A particle moves along the space curve
r
(
t
)
=
⟨
(
1
+
t
)
cos
t
,
(
1
+
t
)
sin
t
,
t
2
⟩
\mathbf r(t)=\langle(1+t)\cos t,(1+t)\sin t,t^{2}\rangle
r
(
t
)
=
⟨(
1
+
t
)
cos
t
,
(
1
+
t
)
sin
t
,
t
2
⟩
. Its velocity is
v
(
t
)
=
r
′
(
t
)
\mathbf v(t)=\mathbf r'(t)
v
(
t
)
=
r
′
(
t
)
, and its angular momentum about the origin is defined as
L
(
t
)
=
r
(
t
)
×
v
(
t
)
\mathbf L(t)=\mathbf r(t)\times\mathbf v(t)
L
(
t
)
=
r
(
t
)
×
v
(
t
)
. What is
L
′
(
t
)
\mathbf L'(t)
L
′
(
t
)
evaluated at
t
=
0
t=0
t
=
0
? a)
⟨
0
,
−
2
,
0
⟩
\langle 0,-2,0\rangle
⟨
0
,
−
2
,
0
⟩
b)
⟨
0
,
2
,
−
2
⟩
\langle 0,2,-2\rangle
⟨
0
,
2
,
−
2
⟩
c)
⟨
0
,
−
2
,
2
⟩
\langle 0,-2,2\rangle
⟨
0
,
−
2
,
2
⟩
d)
⟨
0
,
0
,
1
⟩
\langle 0,0,1\rangle
⟨
0
,
0
,
1
⟩
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