BeginnerTopic 6 of 106Engineering Mechanics
Equilibrium of a particle
A particle is in equilibrium when the vector sum of forces is zero.
In depth
A particle is in equilibrium if ΣFx=0 and ΣFy=0 (and ΣFz=0 in 3D). Three-force problems can be solved with Lamé's theorem or a closed force triangle. Tension in a cable is assumed constant along an ideal pulley.
Key points
- Static means acceleration is zero
- Two equations in 2D
- Check signs for tension vs compression
ExampleA 100 N lamp hanging from two cables at 30° each has tension 100 N in each.
What is Equilibrium of a particle?
A particle is in equilibrium when the vector sum of forces is zero.
Why is it important to understand equilibrium of a particle?
Equilibrium is the condition that a structure or object stays still, and it is the basis of almost every static design check.
Does equilibrium mean nothing is moving?
Equilibrium means the net force is zero, so the acceleration is zero. A body can still move at constant velocity while in equilibrium.
What happens if the forces do not balance?
The body accelerates in the direction of the net force, which is why unbalanced forces must be identified and fixed in design.
How is Equilibrium of a particle used in practice?
Typical applications include checking that a hanging sign is stable under its own weight and wind, ensuring a lifting sling holds a load without moving it and solving the forces on a joint in a frame before sizing its bolts.
What should I learn before Equilibrium of a particle?
Study "Resolving forces into components" first (topic 5 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
What are the key points of Equilibrium of a particle?
Static means acceleration is zero. Two equations in 2D. Check signs for tension vs compression.
Can you give an example of Equilibrium of a particle?
A 100 N lamp hanging from two cables at 30° each has tension 100 N in each.
What comes after Equilibrium of a particle?
The next topic is "Moment of a force", which builds directly on this one.
How difficult is Equilibrium of a particle?
It is classed as Beginner in Engineering Mechanics (topic 6 of 106). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.