15.9 : Torsional Pendulum

A torsional pendulum is a rigid body, like a top, suspended from a string that is assumed to be massless — an assumption that is valid if the rigid body's mass is much larger than the string's mass.

When the top is twisted about the string's axis and released, it oscillates between two angles. The restoring torque is due to shearing of the string.

If the angular displacement is small, the restoring torque can be modeled as proportional to the angular displacement. The proportionality constant is called the string's torsion constant.

The torque can also be written in terms of the rigid body's moment of inertia and angular acceleration.

The two expressions give an equation for simple harmonic motion, with the independent variable being the angle of oscillation, the mass replaced by the moment of inertia, and the force constant replaced by the string's torsion constant.

The angular frequency of the oscillation is then determined, and from it, the time period is derived.