114 Chapt. 12 Rotational Dynamics
for
θ
obtained in the part (d) answer. But we’d still like to Fnd at least a crude estimate
of the time for the pillar to fall down. Make the approximation
ω
=
dθ/dt
≈
Δ
θ/
Δ
t
, set
Δ
θ
=
π/
2, and calculate Δ
t
for a judicious choice of
θ
in
ω
(
θ
). The pillar is 10 m in length.
The result probably has astrophysical accuracy: i.e., factor of 2ish.
012 qfull 01080 3 5 0 tough thinking: rotational anharmonic oscillator
11. You are given an rotational oscillator of rotational inertia
I
obeying an anharmonic oscillator
(AO) torque law
τ
AO
(
x
) =
−
aθ
−
bθ
3
,
where
a
and
b
are positive constants.
a) What is the work
W
AO
done by the AO torque when the oscillator is moved from the origin
to a general point
θ
?
HINTS:
You will have to do an integration. Remember which way
the torque points and which way the oscillator is moving.
b) Say that the oscillator before and after it has been moved was at rest. What was the work
W
app
done by the applied torque that caused the movement? Assume only the applied
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 Fall '06
 Buchler
 Physics, Energy, Force, Kinetic Energy, AO potential energy

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