Chapter 15, Problem 97P

A torsion pendulum consists of a metal disk with a wire running through its center and soldered in place. The wire is mounted vertically on clamps and pulled taut. Figure 15-58a gives the magnitude τ of the torque needed to rotate the disk about its center (and thus twist the wire) versus the rotation angle $\theta$. The vertical axis scale is set by τ_s = 4.0 × 10^-3 N ·m. The disk is rotated to $\theta$ = 0.200 rad and then released. Figure 15-58b shows the resulting oscillation in terms of angular position $\theta$ versus time t. The horizontal axis scale is set by t_s = 0.40 s. (a) What is the rotational inertia of the disk about its center? (b) What is the maximum angular speed d $\theta$/dt of the disk? (Caution: Do not confuse the (constant) angular frequency of the SHM with the (varying) angular speed of the rotating disk, even though they usually have the same symbol $\omega$. Hint: The potential energy U of a torsion pendulum is equal to $\frac{1}{2}$k $\theta$², analogous to U = $\frac{1}{2}$kx² for a spring.)

Figure 15-58 Problem 97