Chapter 7 237 of the motion. If a small white stripe or mirror is attached to the weight, a light can be reflected to a photo-detector and the amplitude and period of the torsional deformation can be measured (Figure 7). The torsional moment of inertia of a cylindrical fiber is: and for an elliptical hair is given by: where a and b are the major and minor semi-diameters of the ellipse forming the cross-section of the hair. Recall that the force required for extension depends on πab. The higher dependence of torsional resistance on dimensions is expected to make torsional properties more dependent on changes occurring in the outer portion of the fiber and more dependent on the properties of the cuticle as mentioned above. Figure 7 illustrates the amplitude motion of a damped torsion pendulum of period, P. The shear storage modulus can be determined from the equation: where ω is the frequency of oscillation (2π/P), l is the fiber length, I t is (π/4)(a3b + b3a) as above, and M is moment of inertia of the rotating weight. Another parameter that can be determined from a torsion pendulum is the log decrement, Δ. Log decrement is related to the log of the change in Figure 7. Illustration of the amplitude of oscillation versus time for a damped torsion pendulum B. ln(a n ) versus n showing exponential decay of peak amplitude for the torsion pendulum illustrated in A.