Period of torsion pendulum from rotational inertia

A torsion pendulum is an angular version of a linear harmonic oscillator: a disk oscillates in a horizontal plane; the reference line oscillates with some angular amplitude. The element of elasticity is associated with the twisting of the suspension wire.

Links:

1. Wikipedia, third formula.

period

The period of pendulum’s oscillations.

Symbol:

T

Latex:

\(T\)

Dimension:

time

rotational_inertia

The rotational_inertia of the disk.

Symbol:

I

Latex:

\(I\)

Dimension:

length**2*mass

torsion_stiffness

The torsion_stiffness, which depends on the properties of the suspension wire.

Symbol:

kappa

Latex:

\(\kappa\)

Dimension:

force*length/angle

law

T = 2 * pi * sqrt(I / kappa)

Latex:

\[T = 2 \pi \sqrt{\frac{I}{\kappa}}\]