Moment of direction

Physical size
Surname	Moment of direction
Formula symbol	${\displaystyle D}$
Size and unit system unit dimension SI N / m M · L 2 · T −2

The Directorate moment , also the restoring torque or target torque is at a mechanical twist the constant of proportionality between the applied torque and the rotation angle : ${\displaystyle D}$ ${\displaystyle {\vec {M}}}$ ${\displaystyle {\vec {\varphi }}}$

${\displaystyle {\vec {M}}=D\cdot {\vec {\varphi }}}$

The directional moment corresponds to the spring constant for longitudinal deflections.

In a system capable of oscillation, for example the balance wheel of a watch, the period of oscillation and the moment of inertia can be used to calculate: ${\displaystyle D}$ ${\displaystyle T}$ ${\displaystyle J}$

${\displaystyle D=4\pi ^{2}\cdot {\frac {J}{T^{2}}}}$

For circular cylindrical wires with the radius and length , the directional moment is proportional to the shear modulus : ${\displaystyle r}$ ${\displaystyle l}$ ${\displaystyle G}$

${\displaystyle D={\frac {\pi \cdot r^{4}}{2}}\cdot {\frac {G}{l}}={\frac {I_{p}\cdot G}{l}}}$

with the polar area moment of inertia . ${\displaystyle I_{p}}$

For example, for a steel wire with the values and you get . ${\displaystyle G_{\mathrm {Fe} }=80\,\mathrm {GPa} ,l=0,1\,\mathrm {m} }$ ${\displaystyle r=2,5\,\mathrm {mm} }$ ${\displaystyle D\approx 50\,\mathrm {Nm} }$

A torque of twists it around: ${\displaystyle M=1\,\mathrm {Nm} }$

${\displaystyle \varphi ={\frac {M}{D}}\approx {\frac {1}{50}}=0,02\,\mathrm {rad} =1,15^{\circ }}$(rad = radian )

See also

• Torsional moment