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60.
(a) Suppose the pendulum is at the angle
θ
with the vertical. The force diagram
is shown to the right.
~
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 Feld 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
τ
=
−
(
mg
−
qE
)
`
sin
θ
.I
f
mg > qE
then the torque is a restoring torque; it tends to pull the pendulum
back to its equilibrium position.
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θ
q
~
E
~
T
m~g
If the amplitude of the oscillation is small, sin
θ
can be replaced by
θ
in radians and the torque
is
τ
=
−
(
mg
−
qE
)
`θ
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics, Force, Gravity

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