What are the two conditions for equilibrium of a rigid body?

Zero resultant force and zero resultant moment about any point.

What happens to a beam on two supports when it is on the point of tilting about one of them?

The reaction at the other support is zero.

How do you choose where to take moments?

About the point where the most unknown forces act, so that they have no moment.

How is a smooth hinge force represented?

By two perpendicular components, H and V, found by resolving.

What forces act on a ladder resting on rough ground against a smooth wall?

Weight, the wall's horizontal normal reaction, and the ground's normal reaction and friction.

What is the friction law?

F\le\mu R, with F=\mu R in limiting equilibrium.

What additional force acts if the wall is rough?

A vertical friction force along the wall, F\le\mu R with R the wall's normal reaction.

What does 'on the point of slipping' tell you?

Friction is limiting, F=\mu R, at every rough contact.

Moments and equilibrium of rigid bodiesEdexcel International A Level Further Maths: Flashcards

Card 1 of 120 of 12 known

Question

What is the moment of a force about a point?

Tap or press Space to reveal

Tap card or press Space to flip

See all 12 cards

What is the moment of a force about a point?: Force $\times$ perpendicular distance from the point to the line of action of the force.
What are the two conditions for equilibrium of a rigid body?: Zero resultant force and zero resultant moment about any point.
Where does the weight of a uniform rod act?: At its midpoint.
What does 'light' mean for a rod or string?: It has negligible mass.
What happens to a beam on two supports when it is on the point of tilting about one of them?: The reaction at the other support is zero.
How do you choose where to take moments?: About the point where the most unknown forces act, so that they have no moment.
How is a smooth hinge force represented?: By two perpendicular components, $H$ and $V$ , found by resolving.
What is the magnitude of the hinge force with components $H$ and $V$ ?: $\sqrt{H^2+V^2}$ .
What forces act on a ladder resting on rough ground against a smooth wall?: Weight, the wall's horizontal normal reaction, and the ground's normal reaction and friction.
What is the friction law?: $F\le\mu R$ , with $F=\mu R$ in limiting equilibrium.
What additional force acts if the wall is rough?: A vertical friction force along the wall, $F\le\mu R$ with $R$ the wall's normal reaction.
What does 'on the point of slipping' tell you?: Friction is limiting, $F=\mu R$ , at every rough contact.

Exam questions on Moments and equilibrium of rigid bodies

A uniform horizontal beam $AB$ of length $6$ m and mass $15$ kg rests on two smooth supports at $C$ and $D$ , where $AC=1$ m and $DB=2$ m. Take $g=9.8$ m s $^{-2}$ .
A particle of mass $3$ kg is now placed at $A$ (and no particle at $B$ ). Find the magnitude of the reaction at $C$ .2 marks
A uniform ladder $AB$ of mass $20$ kg and length $5$ m rests with end $A$ on rough horizontal ground and end $B$ against a smooth vertical wall. The end $B$ is $4$ m above the ground. The ladder is in equilibrium in a vertical plane perpendicular to the wall. Take $g=9.8$ m s $^{-2}$ .
Find the magnitude of the total force exerted by the ground on the ladder.2 marks
A uniform rod $AB$ of mass $9$ kg and length $2$ m is smoothly hinged to a vertical wall at $A$ . The rod is held in equilibrium in a horizontal position by a light string joining $B$ to a point $C$ on the wall, where $C$ is $1.5$ m vertically above $A$ . Take $g=9.8$ m s $^{-2}$ .
Find the tension in the string.3 marks

See the full worksheet

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).