A torsional pendulum is formed by attaching a wire to the center of a meter stick with a mass of 5.00 kg. If the resulting period is 4.00 min, what is the torsion constant for the wire

The torsion constant for the wire is .

Explanation:

The angular frequency of the torsional pendulum (), measured in radians per second, is defined by the following expression:

(1)

Where:

- Torsional constant, measured in newton-meters.

- Moment of inertia, measured in kilogram-square meters.

The angular frequency and the moment of inertia are represented by the following formulas:

(2)

(3)

Where:

- Period, measured in seconds.

- Mass of the stick, measured in kilograms.

- Length of the stick, measured in meters.

By (2) and (3), (1) is now expanded:

If we know that , and , then the torsion constant for the wire is:

The torsion constant for the wire is .