Two conditions for equilibrium of a rigid body?

Resultant force zero, and total moment about any point zero.

Why take moments about a point where an unknown force acts?

That force has zero moment, so it drops out of the equation.

What is the condition for a beam to be about to tilt about a support?

The reaction at the other support is zero.

Which forces act on a ladder against a smooth wall with rough ground?

Weight, horizontal wall reaction, vertical ground reaction, friction at the ground.

In which direction does friction act at the foot of a ladder?

Horizontally, towards the wall.

What does limiting equilibrium mean for the ladder?

F=\mu S at the ground: the ladder is about to slip.

How do you find the centre of mass of a non-uniform rod hanging on two strings?

Take moments about one end using the known tension at the other.

Moments and equilibrium of rigid bodiesEdexcel A-Level Maths: Flashcards

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Define the moment of a force about a point.

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Define the moment of a force about a point.: Force multiplied by the perpendicular distance from the point to the line of action.
What is the unit of moment?: N m
Two conditions for equilibrium of a rigid body?: Resultant force zero, and total moment about any point zero.
Where does the weight of a uniform rod act?: At its midpoint.
Why take moments about a point where an unknown force acts?: That force has zero moment, so it drops out of the equation.
What is the condition for a beam to be about to tilt about a support?: The reaction at the other support is zero.
Moment of a force $F$ at angle $\theta$ to a rod of length $d$ at its end?: $F\sin\theta\times d$
Which forces act on a ladder against a smooth wall with rough ground?: Weight, horizontal wall reaction, vertical ground reaction, friction at the ground.
In which direction does friction act at the foot of a ladder?: Horizontally, towards the wall.
What does limiting equilibrium mean for the ladder?: $F=\mu S$ at the ground: the ladder is about to slip.
Beam 20 kg, 6 m, supports at A and 4 m from A: reaction at A?: $R_A=49$ N
How do you find the centre of mass of a non-uniform rod hanging on two strings?: Take moments about one end using the known tension at the other.

Exam questions on Moments and equilibrium of rigid bodies

A uniform beam $AB$ , of mass 20 kg and length 6 m, rests horizontally on two smooth supports at $A$ and at $C$ , where $AC=4$ m. Take $g=9.8\ \text{m s}^{-2}$ .
A particle of mass $m$ kg is placed on the beam at $B$ and the beam is about to tilt about $C$ . Find $m$ .2 marks
A non-uniform rod $AB$ , of length 4 m and mass 12 kg, is suspended in a horizontal position by two vertical light strings attached at $A$ and $B$ . The tension in the string at $A$ is 50 N. Take $g=9.8\ \text{m s}^{-2}$ .
A particle of mass 5 kg is attached to the rod at its midpoint. Find the new tension in the string at $A$ .2 marks
A uniform rod $AB$ , of mass 8 kg and length 3 m, is hinged at $A$ to a vertical wall. The rod is held in equilibrium in a horizontal position by a light string attached to $B$ and to a point $C$ on the wall above $A$ . The string makes an angle of $40^\circ$ with the rod. Take $g=9.8\ \text{m s}^{-2}$ .
Find the tension in the string.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).