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ch22_p91 - 91(a Suppose the pendulum is at the angle with...

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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 θ = − . 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 θ can be replaced by θ in radians and the torque is
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