The angular momentum of a walking person is plotted as a function of time in the

Question

The angular momentum of a walking person is plotted as a function of time in the figure below which was taken from the Journal of Experimental Biology (J Exp Biol (2008) 211 467-481). The full time scale corresponds to a complete gait cycle (right leg swing followed by left leg swing). The angular momentum shown has been adjusted for size and weight to take into account the size of various individuals who might be part of the study. The graph on the next page from the Journal of Neurophysiology (J Neurophys (2001) 85 1923-1931) shows the flexion of the left knee as a function of time. You have been asked by a physical therapist to use this data and your knowledge of physics to determine at what times in the cycle is there a large net torque on a walking person and where in cycle is the net torque is nearly zero.

Notice that this graph and the graph on the previous page start at different parts of the gait cycle. Although both plots show a full gait cycle, this plot begins at t = 0.8 s and 0% of the gait cycle in the previous plot corresponds to t = 0.3 s for this plot.

Explanation / Answer

torque= changein angular momentum/time

between time 0 to 0.2s

torque= 0.2-(-0.2)/0.2= 2

between 0.2to 0.4

torque= (-0.4-0.2)/0.2=-3

between 0.45 to 0.75 s,

torque = (0.2 -(-0.4))/0.3= 2

between 0.45 and 0.95s

change in angular momentum=0

hence tprque is 0

torque is maximum between 0.2 to 0.4 s

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