15.9: Pendule de torsion et pendule physique
A torsional pendulum is a type of oscillator in which the restoring force is torsion, similar to a simple pendulum. As long as the angular displacement is small, the period is independent of the displacement. In the expression of restoring torque of a torsional pendulum, the variable kappa (κ) is known as the torsion constant of the wire or string, and the unit for the torsion constant can be given by
While torsional pendulums are often used as time-keeping devices, a physical pendulum is any object that can oscillate like a pendulum. The period and angular frequency of a physical pendulum are obtained by considering small-angle approximations, like in the case of a simple pendulum, and rearranging the net torque and moment of inertia equations.
For example, in extreme conditions such as high winds or seismic activity, skyscrapers can sway up to two meters with a frequency of up to 20.00 Hz. Several companies have developed physical pendulums that are placed on the top of skyscrapers. As the skyscraper sways to the right, the pendulum swings to the left, reducing the sway. Assuming the oscillations have a frequency of 0.500 Hz, we can determine the appropriate length of the beam of a pendulum, considering it has a mass of 100 metric tons and a pivot point at one end.
Using the parallel axis theorem, the moment of inertia about the point of rotation is estimated to be ⅓ ML2. Further, using the obtained value of the moment of inertia of the beam and from the equation for the period of a physical pendulum, the length of the beam should be 2.98 m.
This text is adapted from Openstax, College Physics, Section 16.4: The Simple Pendulum and Openstax, University Physics Volume 1, Section 15.4: Pendulums.
