Systems of coplanar forces — A/L Combined Mathematics

What must I remember about Systems of coplanar forces?

• Coplanar Forces: Forces whose lines of action all lie in the same geometric plane.
• Resolution of a Force: A force F acting at angle θ to an axis can be uniquely resolved into two mutually perpendicular components: X = F cos θ along the axis and Y = F sin θ perpendicular to it.
• Resultant of a Coplanar Force System: Sum the resolved components: Rx = ∑ X and Ry = ∑ Y; magnitude of Resultant R = √(Rx² + Ry²); direction tan α = |Ry / Rx|.
• Moment of a Force: The turning effect of force F about point O is M = F * d, where d is the perpendicular distance from O to the line of action of F; taken positive for counterclockwise rotation.
• Varignon's Theorem of Moments: The algebraic sum of the moments of any system of coplanar forces about any point in their plane equals the moment of their resultant about that same point: ∑ Mo(Fi) = Mo(R).

Test yourself (1 minute)

1. Couple definition and properties

   A couple consists of two equal, opposite, and parallel forces whose lines of action do not coincide; moment of a couple is G = F * d (where d is perpendicular arm between forces), INDEPENDENT of the choice of reference point.

2. Equilibrium conditions for Coplanar Forces

   A system of coplanar forces is in equilibrium if and only if: 1) Rx = ∑ X = 0, 2) Ry = ∑ Y = 0, and 3) ∑ Mo = 0 about ANY point.

3. Three non-parallel coplanar forces in equilibrium

   MUST be Concurrent (their lines of action must meet at a single point) and coplanar.

Practise Systems of coplanar forces questions today

Source: NIE G.C.E. (A/L) Combined Mathematics Resource Book - Applied Mathematics, Unit 2

What comes next?

Next in the syllabus

Where does Systems of coplanar forces fit in the syllabus?

Year 2 · Term 2