Statics

Newton's first law can be thought of in two ways.

Firstly, the sum of the forces on an object at constant velocity, which could be stationary, must sum to zero.

$F_{1} + F_{2} + ... = 0$

This works well if the object is considered to be a particle, so cannot rotate

$Σ F_{i} = 0$

Secondly, the sum of the moments of an object that rotates at a constant rate, again at constant velocity which could be stationary.

$M_{1} + M_{2} + ... = 0$

$Σ M_{i} = 0$

These two conditions describe mechanical equilibrium

The second of these is called "the principle of moments".

Questions:

Balanced Forces
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Moments

A moment, $M$ , is defined and the product of the force and the perpendicular distance of the force from a pivot.

$M = F s$ where the force, $F$ is perpendicular to the displacement, $s$ .

If the force and displacement are not perpendicular then the moment of the force is given by $moment = F s sin θ$ where $θ$ is the angle between the force and the displacement.
Or in vector notation

M = F \times s

where the direction of $M$ is perpendicular to both $F$ and $s$ .

GCSE

Moments, Levers and Gears 1 QP [ MS ]
Moments, Levers and Gears 2 QP [ MS ]
Moments, Levers and Gears 3 QP [ MS ]

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AS Level

$F_{1} + F_{2} + ... = 0$

$Σ F_{i} = 0$

$M_{1} + M_{2} + ... = 0$

$Σ M_{i} = 0$

Questions:

Balanced Forces
(Care of isaacphysics.org)

Moments

Equilibrium & Moments Questions OCR AQA Edexcel

Structured Moments Questions

Moments

Moments

Resolving
Moments

Moments
Questions

List
of
Moments
of
Inertia

F1+F2 +...=0

ΣFi=0

M1+M2 +...=0

ΣMi=0

Questions:

Balanced Forces (Care of isaacphysics.org)

Moments

$F_{1} + F_{2} + ... = 0$

$Σ F_{i} = 0$

$M_{1} + M_{2} + ... = 0$

$Σ M_{i} = 0$

Balanced Forces
(Care of isaacphysics.org)