10.6 Torsional Oscillations

If you twist a rope, it will exert a restoring torque, trying to bring itself back to an equilibrium position. This is true of a rope or a steel support. Remember that a torque is a "rotational force". As the disk at the end of the support is twisted one way, the support will try to rotate it back to its equilibrium position.

The resulting torque is proportional to the angle through which the support has been twisted. This proportional restoring force-or restoring torque in this case-is just what we need to have simple harmonic motion.

Figure 10.11 Twisting a fiber or a support will

cause it to exert a restoring torque or "rotational

force". If the fiber or support is attached to an

object that can rotate back and forth, this can

make a torsional pendulum.

As the disk rotates back toward its equilibrium position, it gains kinetic energy and overshoots its equilibrium position. It continues with the support now trying to rotate it back, in the opposite direction. This motion continues and is simple harmonic motion. The period of the motion depends upon the stiffness or strength of the support and upon the moment of inertia of the disk or whatever object is rotating.

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The fact that such a system is a simple harmonic oscillator is important for time-keeping. Being a simple harmonic oscillator means the period is constant. The balance wheel in mechanical watches or clocks is such an arrangement of a rotating wheel attached to a support. In these cases, the support is often in the form of a spring. This is the rotational equivalent of a mass and a spring. Such an arrangement is called a torsional pendulum.

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