9231 · 3.2
Equilibrium of a rigid body flashcards
Revision flashcards for Cambridge 9231 Equilibrium of a rigid body (syllabus 3.2). Flip, recall, then mark a real past-paper question.
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What are the two conditions for a rigid body to be in equilibrium?
1. The vector sum of all external forces acting on the body is zero ($∑ 𝐅 = 𝟎$). 2. The sum of the moments of all external forces about any arbitrary point is zero ($∑ M = 0$).
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What is a rigid body?
An idealisation of a solid body in which deformation is neglected. The distance between any two given points on a rigid body remains constant, regardless of the external forces applied to it.
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What is the Principle of Moments?
For a body to be in rotational equilibrium, the sum of the clockwise moments about any point must be equal to the sum of the anticlockwise moments about the same point.
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What is a 'couple' in mechanics?
A pair of parallel forces of equal magnitude but opposite direction, acting on a body. A couple produces a turning effect (a moment) but no resultant linear force.
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What does 'on the point of tilting' or 'about to rock' imply?
It implies that the normal reaction force at one of the supports has become zero. The body is about to rotate around the other support point, which acts as the pivot.
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What does 'limiting equilibrium' or 'on the point of slipping' mean?
This means the body is about to move, so the frictional force has reached its maximum possible value. This maximum friction is given by $F_{max} = \mu R$, where $\mu$ is the coefficient of static friction and $R$ is the normal reaction force.
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Common Trap: Where does the weight of a 'uniform' rod or ladder act?
For a uniform object, the centre of mass is at its geometric centre. The weight acts vertically downwards through this point.
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Common Trap: What force is often forgotten when a ladder leans against a wall?
The normal reaction force from the wall acting on the ladder. This force acts perpendicular to the wall.
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Why is choosing a pivot point where an unknown force acts a good strategy?
The moment of a force about a point on its line of action is zero. By choosing such a pivot, that unknown force is eliminated from the moment equation, simplifying the problem.
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How do you calculate the moment of a force?
Moment = Force $\times$ perpendicular distance from the pivot to the line of action of the force. Units are Newton-metres (Nm).
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What is the difference between a 'smooth' surface and a 'rough' surface in a mechanics problem?
A smooth surface can only exert a normal reaction force (perpendicular to the surface). A rough surface can exert both a normal reaction and a frictional force (parallel to the surface).