Moments and the Equilibrium of a Rigid Body
Measure the turning effect of a force as force times perpendicular distance from a point, and solve a beam problem by setting both the total force and the total moment to zero.
What a learner can do afterwards
- Find the moment of a force about a point using the perpendicular distance
- Find both support reactions on a loaded uniform beam
- Work out how far a load can move along a plank before it tips
1 · Read
The turning effect of a force is its moment: force times perpendicular distance from the pivot. A 10 N push at right angles 2 m out gives 10 times 2 = 20 N m. With the force fixed, doubling the distance doubles the moment.
A uniform beam 4 m long weighs 40 N and rests on supports at its ends, with a 60 N load at its middle. Total downward load is 40 + 60 = 100 N. Both loads sit centred, so symmetry gives each support 50 N.
A rigid body at rest needs no overall push and no overall twist: resultant force zero and total moment about any point zero. Free body diagrams grow up here to include where each force acts, since the same push twists more from further out.
A uniform 6 m plank weighing 60 N sticks 2 m past a wall edge, so its centre sits 1 m inside with a restoring moment of 60 N m. A 40 N child walking out tips the plank when 40 times d = 60, at d = 1.5 m. At the tipping point the moments match exactly.
Balance every push and every twist, since distance matters as much as force.
2 · Watch
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8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.