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32. (a) A complete revolution is an angular displacement of
Δ
θ
= 2
π
rad, so the angular
velocity in rad/s is given by
ω
=
Δ
/
T
= 2
π
/
T
. The angular acceleration is given by
α
==
−
d
dt
T
dT
dt
2
2
π
.
For the pulsar described in the problem, we have
dT
dt
=
×
×
=×
−
−
126 10
316 10
400 10
5
7
13
.
.
..
s/y
Therefore,
=−
F
H
G
I
K
J
×=
−
×
−−
2
0 033
23 10
13
9
π
(.
)
.
.
s)
rad / s
2
2
The negative sign indicates that the angular acceleration is opposite the angular velocity
and the pulsar is slowing down.
(b) We solve
=
0
+
t
for the time
t
when
= 0:
10
3
0
92
22
8.3 10
s
2.6 10
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 Spring '08
 Any
 Physics, Acceleration

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