A body is in equilibrium if:

- The vector sum of the forces is zero

-The sum of the moments of the forces (about ANY point) is zero

This means that when you resolve (in ANY direction) the sum of the forces going one way equals the sum of the forces going the opposite way. AND the sum of the clockwise moments equals the sum of the anti-clockwise moments (about any point)

The moment of a force (about a point) = Magnitude of the force x Perpendicular distance from the point to the line of action of the force

However you can work with the perpendicular component of a force at an angle, if the perpendicular distance is not obvious.

If the line of action of a force goes through the point then it's moment is 0 because in the equation the distance is 0.

You can use these methods to work out WHERE a force should be applied or WHAT SIZE force should be applied.

If a rigid rod is connected to a wall you can draw the reaction force as a horizontal and a vertical component.

Use \(F_{max}\)=\(\mu\)R if objects are on the point of slipping on a rough surface. R is always perpendicular to the surface, and F always opposes the direction of motion (or the direction the thing will try to move in if it's stationary).

Combine with centre of mass techniques to work out if an object will slip or topple first.

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Mathematics: Mechanics 2 (Notes 1 of 2)