Principle of moments?

For equilibrium, total clockwise moment = total anticlockwise moment about any point.

Two conditions for equilibrium of a rod under parallel forces?

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

A rod whose weight is negligible.

Why take moments about a support?

The reaction there has zero moment, so it is eliminated from the equation.

What is true of a reaction when a rod is about to tilt about the other support?

The reaction at the first support is zero.

How can you check a moments answer?

Take moments about a different point and see if it gives the same result.

Moments of a forceEdexcel International A Level Maths: Flashcards

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Definition of the moment of a force about a point?

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Definition of the moment of a force about a point?: Force $\times$ perpendicular distance from the point to the line of action.
Unit of moment?: Newton metre (N m).
Principle of moments?: For equilibrium, total clockwise moment = total anticlockwise moment about any point.
Two conditions for equilibrium of a rod under parallel forces?: Resultant force is zero and total moment about any point is zero.
Where does the weight of a uniform rod act?: At its midpoint.
What is a light rod?: A rod whose weight is negligible.
Moment of 15 N at 2 m perpendicular distance?: $30$ N m
Why take moments about a support?: The reaction there has zero moment, so it is eliminated from the equation.
What is true of a reaction when a rod is about to tilt about the other support?: The reaction at the first support is zero.
How do you find the weight of a mass $m$ ?: $W=mg$ with $g=9.8$ m s $^{-2}$ .
Uniform plank 4 m, mass 30 kg, on supports at both ends. Reaction at each end?: $\frac{30g}{2}=147$ N
How can you check a moments answer?: Take moments about a different point and see if it gives the same result.

Exam questions on Moments of a force

A light rod $AB$ of length 2 m is horizontal. A vertical force of 15 N acts downwards at $B$ , and a vertical force of 24 N acts upwards at the point $C$ on the rod, where $AC=0.5$ m.
The 24 N force is moved to a point $D$ on the rod, so that the total moment of the two forces about $A$ is zero. Find $AD$ .2 marks
A uniform plank $AB$ of length 4 m and mass 30 kg rests horizontally on two supports, one at $A$ and one at $B$ . Take $g=9.8$ m s $^{-2}$ .
With the man still standing in that position, find the reaction of the support at $A$ .2 marks
A uniform rod $AB$ of length 3 m and mass 8 kg is held in a horizontal position by two vertical light strings, one attached at $A$ and the other attached at the point $C$ on the rod, where $BC=1$ m. Take $g=9.8$ m s $^{-2}$ .
Find the tension in the string 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).