33 Moments Of Forces

A force acting on a body may have a tendency to rotate it. The measure of this tendency is the moment of the force about the axis of rotation. The moment of a force about a specific point equals the product of the magnitude of the force and the normal distance between the point and the line of action of the force. Moment is a vector.

Suppose a force F acts at a point A on a rigid body (Fig. 3.5). For an axis through an arbitrary point O and parallel to the z axis, the magnitude of the moment M of F about this axis is the product of the magnitude F and the normal distance, or moment arm, d. The distance d between point O and the line of action of F can often be difficult to calculate. Computations may be simplified, however, with the use of Varignon's theorem, which states that the moment of the resultant of any force system about any axis equals the algebraic sum of the moments of the components of the force system about the same axis. For the case shown the magnitude of the moment M may then be calculated as

FIGURE 3.5 Moment of force F about an axis through point O equals the sum of the moments of the components of the force about the axis.

where Fx = component of F parallel to the x axis

Fy = component of F parallel to the y axis dy = distance of Fx from axis through O dx = distance of Fy from axis through O

Because the component Fz is parallel to the axis through O, it has no tendency to rotate the body about this axis and hence does not produce any additional moment.

In general, any force system can be replaced by a single force and a moment. In some cases, the resultant may only be a moment, while for the special case of all forces being concurrent, the resultant will only be a force.

For example, the force system shown in Figure 3.6a can be resolved into the equivalent force and moment system shown in Fig. 3.6b. The force F would have components Fx and Fy as follows:

Fy Fiy F2y

The magnitude of the resultant force F can then be determined from

Renewable Energy 101

Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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