# Equilibrium Conditions

You need to check that two conditions are satisfied before you can say that something is in equilibrium.

• The sum of the forces in any direction = 0.

If this is satisfied, the object will have no linear acceleration (for instance, it won't accelerate in any direction).

• The sum of the moments about any point (not just the pivot point) = 0.

If this is satisfied, there is no angular (or circular) acceleration (for instance, the object won't rotate faster or slower.)

We write these two in short hand as:

Look at this. This object is 2m long:

Is this in equilibrium?

Let's apply the Equilibrium Conditions.

Condition 1: Sum of the forces up = Sum of the forces down. Satisfied!

Condition 2: Choose any point to take moments about. I'm going to choose the left hand end of the object.

Clockwise moments: 100N x 2m = 200 Nm

Anticlockwise moments: 70N x 2m = 140 Nm

The moments are not balanced. The object isn't in equilibrium. (See the Moments Learn-it).

(Note: The moment due to the 30N force is zero as its line of action passes straight through the point that we have chosen to take moments about. So we can ignore it!)

Try taking moments about any other point in the same example - for example, the right hand end to prove to yourself that it doesn't matter where you choose, you will still find that it is not in equilibrium.

Question:

Look at the Drawbridge below. Is it in equilibrium? Click on the yes or no options at the bottom to see if you are correct.

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