Defined as the rotating effect of a force applied to an object.
Example: Opening/closing a door applies a force that creates a moment at the hinges.
Formula:
Moment (M) = Force (F) × Perpendicular distance (D)
Example calculation: If F = 4 N, then M = 4 N × D.
Algebraic Sum
The concept of adding numbers where both positive and negative numbers are involved.
Example:
2 + (-1) + 3 = 4
Component Forces
When multiple forces are acting on a body, they can be resolved into a single resultant force.
Example:
Forces P and Q can be resolved into a resultant force R.
P and Q are the component forces of R.
Varignon's Theorem Statement
The theorem states that the moment of a force about a point is equal to the algebraic sum of the moments of its component forces about that point.
Example: Forces P and Q
Consider forces P and Q with resultant R acting about point O.
According to Varignon's Theorem:
Moment of R about O (mR) = Moment of P about O (mP) + Moment of Q about O (mQ).
Scenarios to Consider
Both Forces in Same Direction
If both P and Q cause an anti-clockwise rotation about O:
mP = Anti-clockwise
mQ = Anti-clockwise
Forces Acting in Opposite Directions
If P causes clockwise rotation and Q causes anti-clockwise rotation:
mP = Clockwise
mQ = Anti-clockwise
Sign Conventions
Choose a convention (e.g., clockwise as positive, anti-clockwise as negative) to manage the algebraic sum of moments.
Summary
Varignon's theorem simplifies the analysis of moments by breaking down forces into their components and using algebraic sums to find the resultant moments about a point.