CIE AS Physics (9702) 2019-2021

Revision Notes

5.2.1 Equilibrium of Forces

The Principle of Moments

  • The principle of moments states: For a system to be balanced (in equilibrium), the sum of clockwise moments about a point must be equal to the sum of anticlockwise moments (about the same point)

Principle of moments, downloadable AS & A Level Physics revision notes

Diagram showing the moments acting on a balanced beam

 

  • In the above diagram:
    • Force F2 is supplying a clockwise moment;
    • Forces F1 and F3 are supplying anticlockwise moments
  • Hence: F2 × d2 = F1 × d1 + F3 × d3

Worked example - principle of moments (1), downloadable AS & A Level Physics revision notes

Worked example - principle of moments (2), downloadable AS & A Level Physics revision notes

Exam Tip

Make sure that all the distances are in the same units and you’re considering the correct forces as clockwise or anticlockwise, as seen in the diagram below

 

Clockwise or anticlockwise moment, downloadable AS & A Level Physics revision notes

Equilibrium

  • A system is in equilibrium when all the forces are balanced. This means:
    • There is no resultant force
    • There is no resultant torque
  • An object in equilibrium will therefore remain at rest, or at a constant velocity, and not rotate
  • The system is in an equilibrium state when applying the principle of moments. See “The Principle of Moments” for more notes on this

 

Worked example – Beam in equilibrium

Worked example - beam in equilibrium, downloadable AS & A Level Physics revision notes

Coplanar Forces in Equilibrium

  • Coplanar forces can be represented by vector triangles
  • In equilibrium, these are closed vector triangles. The vectors, when joined together, form a closed path
  • The most common forces on objects are
    • Weight
    • Normal reaction force
    • Tension (from cords and strings)
    • Friction
  • The forces on a body in equilibrium are demonstrated below:

Vector triangle in equilibrium, downloadable AS & A Level Physics revision notes

Three forces on an object in equilibrium form a closed vector triangle

 

Worked example – Forces in equilibrium

Worked example - forces in equilibrium, downloadable AS & A Level Physics revision notes

Exam Tip

The diagrams in exam questions about this topic tend to be drawn to scale, so make sure you have a ruler handy!

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