ROTATIONAL EQUILIBRIUM

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In this course, we assume that muscles act to oppose gravity. This is a good assumption most of the time. We express the assumption in the equation for rotational equilibrium:

The Greek symbol for "sigma" specifies a summation of moments. In other words, in rotational equilibrium, the sum of all the moments that act around a joint's axis is equal to zero:

M₁+M₂+M₃+ ... M_n=0

For example, all the adductor moments are balanced by equal and opposite abductor moments. Flexor moments are balanced by extensor moments.

We can use the equation to calculate the force developed by a muscle to counter a known gravitational resistance.

Let M_m denote the moment produced around a joint by a muscle.
Let M_m denote the moment produced around a joint by gravity. M_m+M_g = 0

M_m = -(M_g)

The "negative" moment merely indicates that its direction is opposite to that of the "positive" moment. If, we decide to designate adduction moments as negative, for example, then abduction moments must be positive.

Because moments are the products of forces and each force's respective moments arms:

F_gs_g=F_ms_m

F_m = (F_gs_g)/s_m

Great, but what's a moment?

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When do we encounter "disequilibrium?"

We don't always activate muscles to counter thte effects of gravtity. Sometimes, we move in such a way that gravity assists our movements, as when we throw a ball from a height like a pitcher's mound, or slam a book downward on the table.

Last updated 7-5-00
© Dave Thompson PT
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