# Regaining balance

## Main Question or Discussion Point

When people are balancing themselves on a surface where their feet do not provide alot of balance (sidestepping a ledge of rope) they tend to wobble or swing their arms to maintain/regain balance. My question is, how does that work? When a person wobbles they move their hips outward and their upper body inward to try and reposition their center of gravity. But wouldn't their center of mass stay the same because of the conservation of momentum? Weight 1 goes one way and weight 2 goes the other way but the center of mass between the two doesn't change.

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There is not a simple two or three sentence answer. Lew Nashner of NeuroCom wrote a paper (together with Paul Cordo from Good Samaritan Hospital) on the arm-waving strategy that should give you all you need. It was published in the Journal of Neurophysiology, 47, in 1982.

Yes, that's it. I'm sorry; I misunderstood what you wanted. For the simple answer, yes, the COG moves. It's seen all the time in force platform measurements.

conservation of momentum doesn't hold here because momentum can be exchanged with the earth by friction on the floor. What is conserved is angular momentum around the point where the feet touch the floor. Wobbling and swaying your arms cannot change that. (but gravity can if the center of mass isn't above the feet)
A very crude model of a person with total mass m and length h is a mass (2/3)m at height (h/2) (hips) and a mass (1/3)m at height h (head+arms). If your hips move to the right with speed v and your head moves to the left with speed v, the angular momentum is (2/3)m * (h/2) - (1/3) h = 0.
The center of gravity will move to the right with speed v/3.

rcgldr
Homework Helper
Balancing with the feet (or one foot) in a fixed position manner is done via a combination of torque and weight shifting. If the COG is off to the left, the mis-aligned downwards force at the COG, and the upwards force at the surface create a counter-clockwise torque. If the person swings his/her arms and/or a leg counter-clockwise, then a reactive clockwise torque is generated, along with a force to the left from the feet (or foot) to the surface which responds with a reactive horizontal force to the right. This combination of torque and horizontal forces are used to correct the offset COG. It's eaiser to do this if a person is holding a long light pole, such as tight rope walkers.

Momentum of person and the earth are conservered if you take into account that the earth is being moved and rotated by any horizontal forces applied to the surface by the person.

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This is very simplified in that we are only considering a person as a single inverted pendulum, albeit a flexible one. It is more correct to look at a double pendulum and to permit varying strategies such as hip, knee, etc, but all that gets way too involved for a post like this.

A person is in balance when his COG falls within his support base (soles of his feet approximately). Ideally, the COG is colinear with the Center of Pressure (COP) of that support, i.e., the resultant of the reaction forces from the floor. If the COP and COG vary enough, the person feels "off balance" and will use one of two mechanisms to correct that: (1) if the COG is within the support area, he can use ankle torque and/or foot shear to move the COP and COG together; (2)2) if the COG is outside the support area, he will use only foot shear to move the COP and COG closer.

Rotating the arms generates a torque that then allows the person to generate an opposing foot shear torque. It is not a terribly effective mechanism and works best when there is only a slight shear force required. One can see newbie ice skaters try this mechanism and fall flat on their keisters when there is insufficient friction (the coefficient of friction for ice is typically less than 0.1) to generate the opposing torque force.

As noted, this is a "quick and dirty" explanation and makes a whole lot of simplifying assumptions, but explains the basics.

rcgldr
Homework Helper
Rotating the arms generates a torque that then allows the person to generate an opposing foot shear torque. It is not a terribly effective mechanism and works best when there is only a slight shear force required.
However this method is good enough for tight rope walkers. Velodrome bicycle racers can balance while not moving, just using the very limited side to side movement of the contact patch with steering inputs. Trials motorcycle riders can balance while not moving using a combination of contact patch movement and swinging one leg.