7.5.A—Describe the properties of a physical pendulum

Describe the properties of a physical pendulum.

• A physical pendulum is a rigid body that undergoes oscillation about a fixed axis.
• For small amplitudes of motion, the period of a physical pendulum is derived from the application of Newton’s second law in rotational form. Relevant equation:
  • i. When displaced from equilibrium, the gravitational force exerted on a physical pendulum’s center of mass provides a restoring torque. Derived equation:
  • ii. For small amplitudes of motion, the smallangle approximation can be applied to the restoring torque. Derived equation: sin
  • iii. The small-angle approximation and Newton’s second law in rotational form yield a second-order differential equation that describes SHM:
• A simple pendulum is a special case of physical pendulums in which the hanging object can be modeled as a point mass at a distance, l, from the pivot point. Relevant equation:
• A torsion pendulum is a case of SHM where the restoring torque is proportional to the angular displacement of a rotating system. For example, a horizontal disk that is suspended from a wire attached to its center of mass may undergo rotational oscillations about the wire in the horizontal plane. Derived equation: