Moment of a force about a point?

Force multiplied by the perpendicular distance to its line of action.

Where is the centre of mass of a freely suspended body in equilibrium?

Vertically below the point of suspension.

How do you show a hinge force?

As unknown horizontal and vertical components, X and Y.

Best point to take moments about?

The point where the most unknown forces act.

Condition for sliding on an incline?

\tan\theta=\mu (friction limiting)

Condition for toppling on an incline?

The vertical through G passes through the lowest edge of the base.

Which happens first, sliding or toppling?

Whichever needs the smaller angle (or force).

What force does a smooth surface exert?

A normal reaction only, no friction.

Foot of a ladder against a smooth wall: S at angle \alpha to the horizontal?

S=\frac{W}{2\tan\alpha}, with F=S and R=W

What do three non-parallel forces in equilibrium do?

Their lines of action meet at a single point.

Equilibrium of rigid bodiesEdexcel International A Level Further Maths: Flashcards

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Two conditions for a rigid body to be in equilibrium?

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Two conditions for a rigid body to be in equilibrium?: Resultant force zero and resultant moment about any point zero.
Moment of a force about a point?: Force multiplied by the perpendicular distance to its line of action.
Where does the weight of a uniform rod act?: At its midpoint.
Where is the centre of mass of a freely suspended body in equilibrium?: Vertically below the point of suspension.
How do you show a hinge force?: As unknown horizontal and vertical components, $X$ and $Y$ .
Best point to take moments about?: The point where the most unknown forces act.
Rod hinged at $A$ , horizontal force $P$ at $B$ , at $\theta$ to the vertical: $P$ ?: $P=\frac W2\tan\theta$
Condition for sliding on an incline?: $\tan\theta=\mu$ (friction limiting)
Condition for toppling on an incline?: The vertical through $G$ passes through the lowest edge of the base.
Which happens first, sliding or toppling?: Whichever needs the smaller angle (or force).
What force does a smooth surface exert?: A normal reaction only, no friction.
Foot of a ladder against a smooth wall: $S$ at angle $\alpha$ to the horizontal?: $S=\frac{W}{2\tan\alpha}$ , with $F=S$ and $R=W$
What do three non-parallel forces in equilibrium do?: Their lines of action meet at a single point.

Exam questions on Equilibrium of rigid bodies

A uniform rod $AB$ of mass $6$ kg and length $2$ m is freely hinged to a fixed point at $A$ . A horizontal force of magnitude $P$ newtons is applied at $B$ , and the rod rests in equilibrium inclined at an angle $\theta$ to the downward vertical, where $\tan\theta=\frac12$ . Take $g=9.8$ m s $^{-2}$ .
Find the angle that the force exerted by the hinge makes with the vertical.2 marks
A uniform solid cylinder of radius $0.2$ m and height $0.6$ m is placed with its circular base on a plane inclined at an angle $\theta$ to the horizontal. The plane is rough. The angle $\theta$ is increased slowly from zero.
The coefficient of friction between the cylinder and the plane is $0.5$ . Find the angle at which the cylinder first begins to move, and state how it moves.2 marks
A uniform ladder $AB$ of mass $20$ kg and length $5$ m rests in equilibrium with its end $A$ on rough horizontal ground and its end $B$ against a smooth vertical wall. The ladder is in a vertical plane perpendicular to the wall, and makes an angle of $60^\circ$ with the horizontal. Take $g=9.8$ m s $^{-2}$ .
Find the magnitude of the frictional force at $A$ .3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).