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# A physical model of human sitting

## Problem

A comfortable sitting position for a patient leaning back on a stool (Figure 1A) requires the weight and torque of the upper half of the body to exactly counterbalance the weight and torque of the lower half of the body. The hips of the patient serve as a pivot point for a simple balance, but they also allow the patient to adjust the angle of his posture, theta, so that he can maintain his balance.
The patient can be modeled as two uniform rods with lengths H (the length from the top of the head to the hips) and L (the length from the hips to the feet) . By changing the angle θ between the torso and legs, the patient can adjust his balance.
Figure 1. The posture of a leaning man sitting balanced on a stool.
Suppose that the patient fails to maintain his balance and tilts off the stool and falls towards the ground. As he falls, his hips remain in contact with the stool without sliding, such that the motion of his head traces a circular arc around the point where his hips make contact with the stool. The patient can avoid hitting the ground only if he adjust the positions of his legs to counterbalance his torso.
When the individual is sitting stationary in Figure 1, the net force acting on the individual points in which direction?