# What are the different uses of torque

## With the definition of the focus_{}

The torque

The amount of torque D is defined as the product of the amount of force and the perpendicular distance a of the line of action to the pivot point:

_{}

The direction of the torque _{}results from the position of the axis of rotation, i.e. stands up vertically _{}and _{}. The torque is thus generally a vector product of the distance vector _{}and strength _{}to indicate:

_{}

The torque is required to describe a rotational movement. If the line of action of force runs through the fulcrum, no rotation takes place (sina = 0). If the force is perpendicular to the radius vector, the drive is most effective.

If several forces act at different points, the torques add up vectorially:

_{}

A rotation does not take place if the sum of all applied torques disappears (torque set)

A body is in equilibrium with regard to rotation when the sum of all acting torques vanishes.

compare translation:

A body is in equilibrium with regard to translation when the sum of all acting forces vanishes.

If a body is suspended in the earth's gravitational field, gravity gdm acts on every mass element dm. The total effective torque results from:

_{}

Since g is a constant factor, it can be drawn in front of the integral (taking into account the commutation rule in the vector product):

_{}

the entire torque can be expressed by

_{}

The total torque results from the cross product of weight and a position vector that points from the axis of rotation to the center of gravity.

A body that is rotatably suspended in the earth's gravitational field behaves as if its entire weight were attacking the center of gravity. If a body is rotatably mounted directly in the center of gravity, the resulting torque is zero. In this case, there is no rotation under the influence of gravity in any position - the body is stable.

__The law of leverage__

A simple application of the torque set is with a two-armed lever (e.g. beam balance):

_{}

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