Rigid-body equilibrium
Objective. Combine force and moment equations.
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- 2. Worked example
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Learn: the key idea
Rigid-body equilibrium occurs when a body experiences no net force and no net turning effect, requiring both the resultant force equation (sum of forces = 0 in each direction) and the resultant moment equation (sum of moments about any point = 0) to be satisfied simultaneously. Combining these equations lets you find unknown forces, such as reactions at supports, alongside unknown positions or distances. Choosing a pivot point that eliminates an unknown force from the moment equation often simplifies the algebra greatly. For example, a uniform beam resting on two supports uses both force balance and moments taken at one support to find both reactions.
Worked example
A uniform rod of weight 20 N and length 4 m rests horizontally on two supports at its ends. Use rigid-body equilibrium to find each support reaction.
- 1By symmetry, weight acts at the midpoint, 2 m from each support
- 2Resolve vertically: R1 + R2 = 20
- 3Take moments about left support: R2 × 4 = 20 × 2, so R2 = 10 N
- 4Substitute: R1 = 20 − 10 = 10 N
Answer: Each support reaction is 10 N
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Start practisingCommon mistake. Students use only the force equation and ignore the moment equation, so they cannot find separate reactions when there are two or more support forces. Always include a moment equation when there is more than one unknown force.
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