4.2 Equilibrium of forces

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.

Static equilibrium requires ΣF=0 and Στ=0. The body has no linear acceleration and no angular acceleration in the chosen frame.

Check force balance in each independent direction, then check moments about a convenient point. Satisfying one condition alone is insufficient.

A beam can have clockwise and anticlockwise moments balanced yet still accelerate sideways if a horizontal resultant force remains.

Zero resultant force does not prevent rotation, and zero resultant torque does not prevent translation.

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.