Force times the perpendicular distance from the point to the line of action, in N m.

Two conditions for equilibrium of a rigid body?

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

Centre of mass in two dimensions?

\bar x=\frac{\sum mx}{\sum m} and \bar y=\frac{\sum my}{\sum m}

Why does g cancel in centre of mass calculations?

It multiplies every weight, so it appears on both sides and divides out.

What is the common error in finding a centre of mass?

Dividing by the number of particles instead of the total mass.

How do you remove a particle from a system?

Subtract its m, mx and my from the totals.

Where is it best to take moments?

About the point where an unknown force acts, so that force drops out.

Moments and centres of mass of discrete massesEdexcel A-Level Further Maths: Flashcards

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Moment of a force?

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Moment of a force?: Force times the perpendicular distance from the point to the line of action, in N m.
Two conditions for equilibrium of a rigid body?: Resultant force is zero and total moment about any point is zero.
Where does the weight of a uniform rod act?: At its midpoint.
Centre of mass of particles on a line?: $\bar x=\frac{\sum mx}{\sum m}$
Centre of mass in two dimensions?: $\bar x=\frac{\sum mx}{\sum m}$ and $\bar y=\frac{\sum my}{\sum m}$
Why does $g$ cancel in centre of mass calculations?: It multiplies every weight, so it appears on both sides and divides out.
What is the common error in finding a centre of mass?: Dividing by the number of particles instead of the total mass.
How do you remove a particle from a system?: Subtract its $m$ , $mx$ and $my$ from the totals.
Where is it best to take moments?: About the point where an unknown force acts, so that force drops out.
What happens at a support when a rod is about to tilt?: The reaction there is zero.
Centre of mass of 1 kg at $x=0$ and 3 kg at $x=8$ ?: $\frac{0+24}{4}=6$
What is the centre of mass if all masses are equal?: The mean of the positions.

Exam questions on Moments and centres of mass of discrete masses

Three particles of masses 2 kg, 3 kg and 5 kg are placed on a straight line at the points $x=1$ m, $x=4$ m and $x=9$ m respectively, where $x$ is the distance from a fixed origin $O$ on the line. Take $g=9.8$ m s⁻².
Find the total moment of the weights of the three particles about $O$ .2 marks
Four particles of masses 1 kg, 2 kg, 3 kg and 4 kg are placed at the points with coordinates $(0,0)$ , $(5,0)$ , $(4,3)$ and $(1,3)$ respectively, where distances are in metres.
Find the distance between the centre of mass and the 2 kg particle.2 marks
A uniform rod $AB$ has length 6 m and mass 12 kg. It rests horizontally on two smooth supports at $C$ and $D$ , where $AC=1$ m and $DB=2$ m. Take $g=9.8$ m s⁻².
Find the magnitudes of the reactions at $C$ and $D$ .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).