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91. (a) Suppose the pendulum is at the angle
θ
with the vertical. The force diagram is
shown below.
G
T
is the tension in the thread,
mg
is the magnitude of the force of gravity,
and
qE
is the magnitude of the electric force. The field points upward and the charge is
positive, so the force is upward. Taking the angle shown to be positive, then the torque on
the
sphere
about
the
point
where
the
thread
is
attached
to
the
upper
plate
is
()
sin
mg
qE L
τ
=−
−
.
If
mg
>
qE
then the torque is a restoring torque; it tends to pull
the pendulum back to its equilibrium position.
If the amplitude of the oscillation is small, sin
can be replaced by
in radians and the
torque is
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This note was uploaded on 01/25/2011 for the course PHYSICS 17029 taught by Professor Rebello,nobels during the Fall '10 term at Kansas State University.
 Fall '10
 Rebello,NobelS
 Force, Gravity

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