Example 11  Pendulum Motion and Walking

When we walk, our legs alternately swing forward about the hip joint as a pivot. In this motion the leg is acting approximately as a physical pendulum. Treating the leg as a uniform rod of length D=0.80 m, find the time it takes for the leg to swing forward.

Reasoning  The time it takes for the leg to swing forward is one-half of the period T, which is related to the frequency f by f=1/T (Equation 10.5). For a physical pendulum the frequency is given by (Equation 10.15), where the moment of inertia for a thin rod of length D rotating about an axis perpendicular to one end is given in Table 9.1 as . In Equation 10.15 the length L is the distance between the pivot at the hip and the center of gravity of the leg. Since we are treating the leg as a thin uniform rod, the center of gravity is at the center and L=0.40 m.

Solution Using Equations 10.5 and 10.15, we find that the period is

Substituting the moment of inertia of the thin rod into this result gives
The desired time is one-half of the period or .



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