When a person walks, the only force acting on him is the force of friction between him and the ground (neglecting air resistance and all). The magnitude of acceleration due to this force is independent of the mass of the object (longer legs have more mass). Hence the person should move with with a velocity independent of the length of his legs.
But I have heard (also observed) that people with longer legs walk faster than ones with shorter legs. If that is true, then why?
One can argue that the torque about the pivot due to friction is more in case of longer legs, But then the torque due to gravity (when one raises his leg to move), which opposes the frictional torque, is also more for longer legs. And why would these torques make a difference anyway, as they have no effect on the acceleration of the center of mass?
Best Answer
I think the simplest model that may be useful here is to treat the legs as simple pendula. In "steady state" comfortable walking, it is reasonable to assume that the legs oscillate close to their natural frequency. That is, the forward contacting leg lifts allowing the rear to swing forward freely over the stride. For a (simple) pendulum with:
$$\omega = \sqrt{\frac{g}{l}}$$ the velocity along the ground will be: $$v \propto l\omega = \sqrt{lg}$$
Note that this result is independent of the mass of the walker and the ground contact forces.