Force: Moments of a Force & Equilibrium

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Moment of a Force

Force multiplied by the perpendicular distance to the fulcrum

M = Fd

Vector quantity

Unit = Newton metre (Nm)

Fulcrum is a fixed point about which a rigid body is free to rotate

The moment of a force can only be determined with reference to an axis

Lever

A rigid body that is free to rotate about a fixed axis

We most often deal with levers that pivot on a point, which is called the fulcrum

Levers convert a small force applied over a long distance to a large force applied over a small distance

Examples:

Door handle

Forearm pivots at the elbow

Couple

A pair of equal and opposite forces whose lines of action do not coincide

When a couple acts on a body, the resultant force is zero, but it has a turning effect

Example: the forces exerted by one's hand on a screw-driver

Torque

The torque of a couple is equal to the magnitude of one of the forces multiplied by the distance between them

T = Fd

Examples of torques are twisting a tap or the handle bars of a bicycle

Conditions for Equilibrium

A body is in equilibrium when it is neither accelerating nor changing its rate of rotation

Two conditions must be satisfied:

The vector sum of the forces in any direction is zero

The vector sums of moments about any points is zero (AKA the principle of moments)

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