Require both force and moment balance for equilibrium
Check translation and turning separately before declaring a supported object in equilibrium.
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Calculate a resultant force.
- Identify opposing and adding moments.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is the resultant of 15 N upward and 10 N downward?
What you will learn
- State both conditions for equilibrium.
- Reject examples with either an unbalanced force or an unbalanced moment.
Two independent checks are needed
An object is in equilibrium when its resultant force is zero and its resultant moment is zero. The first condition removes translational acceleration; the second removes angular acceleration. For an object initially at rest, both conditions support continued rest in the stated ideal conditions. Zero acceleration should not be confused with proof that an initially moving object has stopped.
A 10 N downward force and a 10 N upward force along the same vertical line have zero resultant and, about any pivot, cancelling moments. Separate their parallel lines by 0.40 m instead and their forces still cancel, but the two 10 N forces produce a net turning effect of 4.0 N m. Force balance by itself is therefore insufficient.
Zero turning effect alone is also insufficient
An upward 15 N force and downward 10 N force on the same line through a chosen point each have zero moment about that point. Their resultant is 5 N upward, so the object is not in complete equilibrium. Finding one convenient point where a net moment vanishes is not a substitute for the force check.
For a supported beam at rest, list all downward loads and beam weight, then find the required support force as well as checking opposing moments. State the initial-rest and maintained-support conditions. Static equilibrium describes the resting balance; neither condition is a claim that a support of any real strength can carry any imagined load safely.
Sources for this lesson
Pause and explain
Equal opposite forces act on different parallel lines. Does zero resultant force alone prove equilibrium?
Worked example
Two opposite 10 N vertical forces act on separate parallel lines 0.40 m apart. Is the object in equilibrium?
Show the worked solution
- Their vector sum is zero.
- Taking moments about one force line leaves the other moment 10 × 0.40 = 4.0 N m.
- The non-zero resultant moment means the object is not in equilibrium.
Answer No; resultant force is zero but resultant moment is 4.0 N m.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
For opposite 10 N vertical forces separated by 0.40 m, check force and moment balance.
Give me a hint
Take moments about one force line so that force has zero lever arm.
Compare my reasoning
- Resultant force = 10 − 10 = 0 N.
- The other force gives moment 10 × 0.40 = 4.0 N m.
- The object fails the moment condition for equilibrium.
Zero resultant force; 4.0 N m resultant moment; not equilibrium.
Look for these in your work
- Use both balance conditions.
- Identify the separated force lines.
For 15 N up and 10 N down on one line through a chosen point, find the resultant and moment about that point. Decide if equilibrium holds.
Give me a hint
A force through the chosen point has zero moment but can still change motion.
Compare my reasoning
- Resultant force = 15 − 10 = 5 N up.
- Both forces pass through the point, so moment about it is zero.
- The non-zero force prevents complete equilibrium.
5 N upward; zero moment about the point; not equilibrium.
Look for these in your work
- Keep force and moment conclusions separate.
- Explain the failed condition.
A beam initially rests with zero resultant force and zero resultant moment under maintained loads and support. Explain what the two statements justify and why an initially moving object needs more context.
Give me a hint
Separate no acceleration from a claim about the existing motion.
Compare my reasoning
- Zero resultant force removes translational acceleration.
- Zero resultant moment removes angular acceleration in the stated model.
- Initial rest therefore persists, while no acceleration alone does not establish that pre-existing motion has stopped.
Initial rest persists under maintained balance; zero acceleration alone does not prove an already moving object is at rest.
Look for these in your work
- State the initial condition.
- Explain both kinds of balance.
Common mistakes
- Check both resultant force and resultant moment.
- Opposite forces on different lines can still turn an object.
- Zero acceleration does not establish initial rest.
What can you explain now?
Is zero resultant moment sufficient for equilibrium?
Compare with the explanation
No; resultant force must also be zero.
The translational and rotational conditions must both hold.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Give one force-balanced example that still turns, and one zero-moment example that still has a resultant force.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.