Question

 A torsional pendulum is formed by attaching a wire to the center of a meter stick with mass 2.0 kg. If the resulting period is 3.0 minutes, what is the torsion constant for the wire?

Answer 1

The period of the torsional pendulum is:

$$T = 2\pi\sqrt{\dfrac{I}{\kappa}}$$

where $I$ is the moment of inertia, and $\kappa$ is the torsion constant. The moment of inertial of the meter stick ($l = 1m$) about its center is:

$$I = \dfrac{ml^2}{12}$$

where $m = 2kg$ is the mass of the stick. Substituting this into the first formula and expressing $\kappa$, find:

$$\kappa = \dfrac{\pi^2l^2m}{3T^2}$$

since $T = 3min = 180s$, obtain:

$$\kappa = \dfrac{\pi^21^2\cdot 2}{3\cdot 180^2} \approx 2.03\times 10^{-4} m^2\cdot kg/s^2$$

Answer. $2.03\times 10^{-4} m^2\cdot kg/s^2$.