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.
More to read
12.1 Conditions for Static Equilibrium
A rigid body needs two things for true rest: no overall push and no overall twist. This page states both conditions and shows how to use them.
Free body diagrams grow up here to include where each force acts. The same force twists more when it grips further from the pivot.
Summary
The chapter summary lines up every statics result in one place. Equilibrium conditions, centre of gravity and the problem solving steps all appear together.
Read it last, not first. Tick off each idea against a worked example to prove you can use it, not just recite it.
10.3 Dynamics of Rotational Motion: Rotational Inertia
Spin has its own version of mass called rotational inertia. It explains why the same twist spins a light wheel faster than a heavy one.
The link to moments is direct: torque plays the role of force in turning. Compare each linear idea with its rotational twin as you read.
Conceptual Questions
These questions poke at the ideas without numbers. They ask why doors have handles far from hinges and why tightrope walkers carry poles.
Argue each answer out loud before checking. If the words will not come, the concept needs another look.
Explore more
2 · Watch
En anglaisTake it off screen
Where it sits
Learn first
Optional connections
This opens up
14 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.