Moment (technical mechanics)

In technical mechanics, the moment describes the effect of a vector quantity acting on a point ( bound vector , e.g. a force). This includes, among other things, the moment of momentum (distance times momentum ) or the moment of a force (distance times force ) and the moment of a couple of forces (also distance times force). The moment of area, on the other hand - which also plays an important role in mechanics - is a cross-sectional parameter in bar statics.

In technical mechanics, a distinction is made primarily between the “moment of a force” and the “moment of a force couple”.

Moment of a force

Force around a reference point

The vector of the torque results from the cross product of the position vector and the force vector: ${\displaystyle {\vec {M}}}$

${\displaystyle {\vec {M}}^{(A)}={\vec {r}}\times {\vec {F}}}$

It is the position vector from the reference point of the torque to the point of application of force. The direction of the torque vector indicates the direction of rotation of the torque. ${\displaystyle {\vec {r}}}$

In the plane, the moment of a force with respect to a point results from the shortest perpendicular distance between the reference point and the line of action of the force and the amount of the force as: ${\displaystyle M}$ ${\displaystyle A}$ ${\displaystyle a}$ ${\displaystyle F}$

${\displaystyle M^{(A)}=a\cdot F}$

In technical mechanics, it is also referred to as moment of force or polar moment of force with respect to a point. Details can be found under the term torque, which is commonly used in physics . In technical mechanics, however, a torque is usually understood to be a moment that causes a rotation, for example on a screw or a (motor) shaft .

Moment of a couple of forces

→ Main article : Couple of forces

Power couple

The moment of a parallel pair of forces results from the amount of one of the two forces and the distance between the two forces: ${\displaystyle M}$ ${\displaystyle F}$ ${\displaystyle a}$

${\displaystyle M=a\cdot F}$

In contrast to the moment of a force, the moment of a force couple does not refer to a reference point. In the mechanics of rigid bodies, a couple of forces can be completely replaced by a corresponding moment. A single force, on the other hand, cannot be replaced by its moment.

Web links

Wiktionary: moment # noun, n  - explanations of meanings, word origins, synonyms, translations

literature

• Istvan Szabó : Introduction to Technical Mechanics , Springer, 1999, ISBN 3-540-44248-0 ( limited preview , accessed April 25, 2013).
• Peter Gummert, Karl-August Reckling: Mechanik , Vieweg, 1994, ISBN 3-528-28904-X .

Individual evidence

1. ↑ P. Eberhard, M. Hanss: Technische Mechanik 1 , Systems of Bound Vectors, Institute for Technical and Numerical Mechanics ( online ( Memento of the original from September 22, 2013 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this note. (PDF; 132 kB), accessed on July 17, 2013) 
2. ^ Gross, Hauger, Schröder, Wall: Technische Mechanik - Statik , Springer, 11th Edition, 2011, pp. 40–56.
3. ↑ Mahnken: Textbook of Technical Mechanics - Statik , Springer, 2012, pp. 97-104.
4. ↑ Christian Spura: Technische Mechanik 1 - Sterostatik , Springer, 2016, pp. 42f., 45.
5. ^ Richard, Sander: Technische Mechanik - Statik , Springer, 5th edition, pp. 33, 39–41.
6. ↑ Dankert, Dankert: Technische Mechanik , Springer, 7th edition, pp. 19–24.