Moment of a force:
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The moment of a force about a point is product of the force and perpendicular distance of the line of it action from the point.
If F be the force and p the perpendicular distance of the line of action from fixed point O, then the moment of F about O = F x p.
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- Positive and Negative Moments: The moment of the force about a point measures the tendency of the force to cause rotation about that point. If tendency of force is to turn lamina in anti clockwise direction then usual convention is to regard the moment as positive and that in clockwise direction as negative.
- The algebraic sum of moments of a set of forces about a given point is sum of the moments of forces, each moment having the proper sign of it prefixed to it.
- The algebraic sum of moments of any 2 forces about any point in their plane is equal to moment of their resultant about the same point.
- If any number of forces in 1 plane acting on a rigid body has a resultant, the algebraic sum of their moment about any point in their plane is equal to the moment of their resultant.
- The moment of a force about an axis is product of resolved part of the force in a direction perpendicular to axis (other component being the product of force parallel to the axis and the shortest distance between axis and line of force.
Example: The beam AB which is uniform is 18 feet long and weighs 30 lb. Having masses of 20 and 45 lb are suspended from A and B respectively. At what point should the beam be supported so that it can rest horizontally?
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Solution: Let the weight of beam AB have at its middle point C. when the masses of 20 and 45 lb are suspended from A and B respectively, then let the resultant of these 3 passes through O.
As, AB = 18 ft => AC = BC = 9ft
Let CO = x ft, then AO = (9 + x) ft and
BO = (9 - x) ft
As, the resultant passes through O, thus moments of the acting force at the point A, B and C about O will be zero.
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