Moment of Force about a Point in Space

Moment of Force about a Point in Space

Moment of force about a point in three dimensions is a vector quantity given by

where is a vector from the point about which moment is taken to any point on the line of action of force.

Consider a force of magnitude F acting from A (x1, y1, z1) and B (x2, y2, z2)) as shown in Fig. 3.11.1. The moment of this force about a point C will be

Solved Examples for Understanding

Example 3.11.1 

A force acts at a point P(4, 3, 2) m. Determine the moment of this force about the point Q(2, 3, 4) m in vector form. Also find the magnitude of the moment and its angles with respect to x, y, z axes.

Solution : 

Example 3.11.2 

Determine the moment of the force F shown in Fig. 3.11.2 about the origin.

Solution: 

The required co-ordinates are A (− 3, 6, – 2), B (5, 9, – 3)

Example 3.11.3 

For the previous example, find moment of the force F about point P.

Solution :

Example 3.11.4 

A force acts at point A (1,2,3). Find a) Moment of the force about origin b) Moment of force about B (2, 1, 2) c) Component of this force along line AB.

Solution: 

Example 3.11.5 

Two forces F1 = 500 N and F2 = 600 N act along AB and AC as shown in Fig. 3.11.3. Determine the moment of the resultant of F1 and F2 about O.

Solution: 

The required co-ordinates are A (0, 10, 0), B (−, 1, 0, 5), C (6, 0, 2).

Example 3.11.6 

A rectangular plate is supported by brackets to the wall at A and B and host wire CD as shown in Fig. 3.11.4. Knowing that tension in wire is 200 N determine the moment about point A, of the force exerted by wire on point 'C'.

Solution: