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It is said that walking at a comfortable speed

2.  It is said that walking at a comfortable speed involves a pendulum-like motion of your legs.  We want to see how good this claim is quantitatively.   

    (A) First we are going to predict your gait.   The legs are not a SIMPLE pendulum, in that all the mass is not concentrated at your foot, but is distributed.    For such a pendulum the period T is given by the equation  T = 2π √(I/mgL) where I is the moment of inertia.   m is the mass of the pendulum; L is its length.   As you recall, for a uniform rod,   I=1/3 mL 2   This is a tough estimation because you know your leg has more mass at the thigh than the ankles, but for the moment, it's going to be our best guess.     Now m is not your whole mass, but the mass of your leg, which is typically about 5% of your m.   So, with a ruler and a scale, make a PREDICTION of the period of your leg as it swings in a walking motion.

    (B)  CHECK your prediction!    Time yourself (or do it with a friend, more fun) walking 20 steps.    Now there's just one more little trick here.   If you watch carefully, a "step" is only half a cycle, since the leg must then swing back.   So 20 steps = 10 cycles.   Take the time you measure for 20 steps, divide by 10, and see if you are any where near the prediction from part A.  

Note that because of your length of leg and weight, everybody can have a different answer to this question!

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