Moments of Forces

Introduction

A moment of a force is essentially it's turning effect about a pivot point. In this learn page we will define the moment of a force, and how we can apply it to problems, in order to work out unknowns etc.

The Moment of a Force

The moment of a force is defined as it's magnitude multiplied by it's perpendicular distance to a chosen pivot point. This is the perpendicular distance from the line of action of the force, to the pivot point, as shown by the diagram below.
What's often forgotten is that it is the perpendicular distance (to the line of action of the force) that is multiplied by the magnitude of the force! (d=perpendicular distance)

If the perpendicular distance is unclear remember that the force is a vector. You can therefore split it into two components, one horizontal and one vertical. This will allow you to work out the moments of each of the components with ease.

Tipping and Toppling

Tipping

An object at rest with a force applied to it can tip if the moment of the force applied, about a given pivot point, is greater than the moment of the objects weight about the same pivot point. Therefore for tipping to occur:

If you take moments about the pivot point for the situation described above there will be a net anti-clockwise moment. This causes the object to tip up.

Toppling

Toppling happens when the line of action of the weight vector of an object lies outside it's base. But what does this really mean? Well the weight vector of an object will always point directly downwards from the centre of mass (we always work on earth in this module, and always orientated properly!). So if the object sits on a sufficiently tilted bank, it's weight will inevitably lie past it's base.

Solutions

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