4.2 Equilibrium of forces
- Syllabus
- 9702–2028–2029
- Topic
- 4.2
- Level
- AS
Learning objectives
4.2.1The principle of moments• state and apply the principle of moments4.2.2That, when there is no resultant force and no resultant torque, a system is• understand that, when there is no resultant force and no resultant torque, a system is in equilibrium4.2.3A vector triangle to represent coplanar forces in equilibrium• use a vector triangle to represent coplanar forces in equilibrium
In rotational equilibrium, clockwise and anticlockwise moments about a pivot balance
The principle of moments states that if a body is in equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments.
Choose a convenient pivot, use perpendicular distances and take a consistent sign convention. A force through the pivot has zero moment.
A 20 N load 0.40 m from a pivot is balanced by a 10 N load at 0.80 m on the opposite side.
Moment balance alone does not guarantee translational equilibrium; the resultant force must also be zero.
Equilibrium requires zero resultant force and zero resultant torque
ΣF=0andΣτ=0
When both conditions hold, there is no linear acceleration and no angular acceleration. The object may be stationary or may move with constant velocity without changing its rotational state.
Resolve forces in each independent direction, then take moments about a convenient point. Satisfying either condition alone is insufficient.
Balanced clockwise and anticlockwise moments do not stop sideways acceleration if a horizontal resultant remains. Conversely, zero resultant force can coexist with a non-zero couple and angular acceleration.
Equilibrium means no acceleration, not necessarily no motion. Always test translation and rotation separately.
A vector triangle can show three coplanar forces in equilibrium
For three coplanar forces in equilibrium, placing their vectors head-to-tail forms a closed triangle because their vector sum is zero.
Keep each vector’s direction and scale, then use the triangle or sine rule to relate unknown magnitudes. A closed shape is a force-balance test.
For a symmetric load supported by two equal strings, the two tension vectors and the weight close to a triangle.
A force triangle represents vector addition, not the physical shape of the object or the path of motion.