Twist

This article deals with the rotary thrust in gyro theory. For the twisting shot in the shot put see there.

The rotational shock is in the gyro theory the result of torque and the duration of exposure to a body . Both the amount and the direction of the moment play a role. The dimension of the rotary impact is M · L ² · T ^-1 , its SI unit is N · m · s . ${\displaystyle \Delta {\vec {L}}}$

According to the principle of twist , a moment causes a corresponding change in angular momentum: ${\displaystyle {\vec {M}}}$

${\displaystyle {\dot {\vec {L}}}={\vec {M}}}$

With

• the angular momentum ${\displaystyle {\vec {L}}}$
• the time derivative over point .

If the moment is (with ) constant in the time interval , the rotary shock results ${\displaystyle \Delta t:=t_{2}-t_{1}}$ ${\displaystyle t_{1}<t_{2}}$

${\displaystyle \Delta {\vec {L}}={\vec {M}}\cdot \Delta t}$

With a general curve of the moment over time, the rotary shock results from an integral over time:

${\displaystyle \Delta {\vec {L}}=\int _{t_{1}}^{t_{2}}{\vec {M}}\,\mathrm {d} t}$

Angular momentum is applied to a resting body by a corresponding rotary shock. Conversely, a rotary shock occurs when angular momentum is instantly destroyed. Angular momentum change and rotary shock are in the same direction, but this does not always apply to the axis of rotation . If the rotary impact does not take place in the direction of a main axis of inertia , then a rigid body then circles around a straight line deviating from the impact axis, see ellipsoid of inertia .

This effect is explained by the anisotropy of the rigid body with respect to rotary movements: the asymmetrical top is double anisotropic, the symmetrical one is simply anisotropic, and only the spherical top with the same moments of inertia around all axes is isotropic.

See also

• Impulse # impulse
• Shock (physics)

Individual evidence

1. ↑ Grammel (1920), p. 16, Magnus (1971), p. 47, see literature.
2. ↑ Grammel (1920), p. 16.
3. ↑ Grammel (1920), p. 43.

literature

• K. Magnus : Kreisel: Theory and Applications . Springer, 1971, ISBN 978-3-642-52163-8 , pp. 47 ( limited preview in Google Book Search [accessed February 20, 2018]).
• R. Grammel : The top . Its theory and its applications. Vieweg Verlag, Braunschweig 1920, DNB  451641280 , p. 16 ( archive.org - "swing" means angular momentum and "torsional balance" means rotational energy).