Equilibrium (Cambridge (CIE) O Level Physics): Revision Note

The Principle of Moments

• The term equilibrium means that an object keeps doing what it’s doing, without any change

• Therefore:

  • If the object is moving it will continue to move (in a straight line)

  • If it is stationary it will remain stationary

  • The object will also not start or stop turning

• The above conditions require two things:

  • The forces on the object must be balanced

    • There must be no resultant force

  • The sum of clockwise moments on the object must equal the sum of anticlockwise moments

    • there must be no resultant moment

A Moving Car and a Balanced Beam in Equilibrium

When the forces and moments on an object are balanced, the object will remain in equilibrium

• If the above two conditions are met, then the object will be in equilibrium

The Principle of Moments

• The principle of moments states that:

  If an object is balanced, the total clockwise moment about a pivot equals the total anticlockwise moment about that pivot

• Remember that the moment = force × distance from a pivot

• The forces should be perpendicular to the distance from the pivot

  • For example, on a horizontal beam, the forces which will cause a moment are those directed upwards or downwards

Demonstrating Equilibrium

• A simple experiment to demonstrate that there is no net moment on an object in equilibrium involves taking an object, such as a beam, and replacing the supports with newton (force) meters:

Forces on a Beam

Several forces act on a supported beam, including the mass of the beam and the mass of an object suspended from it

• The beam in the above diagram is in equilibrium

• The various forces acting on the beam can be found either by taking readings from the newton meters or by measuring the masses (and hence calculating the weights) of the beam and the mass suspended from the beam

• The distance of each force from the end of the ruler can then be measured, allowing the moment of each force about the end of the ruler to be calculated

• It can then be shown that the sum of clockwise moments (due to forces F₂ and F₃) equal the sum of anticlockwise moments (due to forces F₁ and F₄)

More detail on setting up this experiment

• Use a meter ruler for the beam

• Suspend it via two Newton meters, one on each side, that each hang from a clamp stand

• F₁ is the reading given on the left side Newton meter and F₄ is the reading given on the right

• Create a loop of string, tie a tight knot and slide the ruler through it

• F₃ will be the weight of a mass hook with 10 N weights suspended from this string

• F₂ is the weight of the beam