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Cartesiaanse vorm voor vectorformulering

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The moment of force is defined as the cross-product of position and force vectors.

The cross-product for the moment can be expressed in the determinant form, using unit vectors and the Cartesian form of position and force vectors.

The determinant is expanded to determine the Cartesian vector formulation of the moment of force.

Consider that a force of 10 N is applied to a revolving door at a point given by the position vector in the cartesian components form. Here, the moment of force in the vector formulation needs to be determined.

In this case, the force vector is perpendicular to the y-z plane , which results in the y and z components of the force vector being zero. A determinant is constructed using the position vector and the force vector.

Finally, by expanding the determinant, the revolving door's moment of the force about the z-axis is determined.

Here, the moment is in the positive z-direction, implying the door rotates counterclockwise.

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Vector Formulation

Position Vector

Determinant Form

Vector Components

Static Equilibrium