Equilibrium (Cambridge O Level Physics)

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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

Equilibrium, IGCSE & GCSE Physics revision notes

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

Worked example

A parent and child are at opposite ends of a playground see-saw. The parent weighs 690 N and the child weighs 140 N. The adult sits 0.3 m from the pivot.

Principle of Moments Worked Example GCSE, downloadable IGCSE & GCSE Physics revision notes

Calculate the distance the child must sit from the pivot for the see-saw to be balanced.

Answer:

Step 1: List the know quantities

  • Clockwise force (child), Fchild = 140 N
  • Anticlockwise force (adult), Fadult = 690 N
  • Distance of adult from the pivot, dadult = 0.3 m

Step 2: Write down the relevant equation

  • Moments are calculated using:

Moment = force × distance from pivot

  • For the see-saw to balance, the principle of moments states that

Total clockwise moments = Total anticlockwise moments

Step 3: Calculate the total clockwise moments

  • The clockwise moment is from the child

Momentchild = Fchild × dchild = 140 × dchild

Step 4: Calculate the total anticlockwise moments

  • The anticlockwise moment is from the adult

Momentadult = Fadult × dadult = 690 × 0.3 = 207 Nm

Step 5: Substitute into the principle of moments equation

140 × dchild = 207

Step 6: Rearrange for the distance of the child from the pivot

dchild = 207 ÷ 140 = 1.48 m

Examiner 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 belowClockwise or anticlockwise moment, downloadable AS & A Level Physics revision notesClockwise is defined as the direction the hands of a clock move (and anticlockwise as the opposite)IGCSE & GCSE Maths revision notes

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

Demonstrating equilibrium, IGCSE & GCSE Physics revision notes

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

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Leander

Author: Leander

Expertise: Physics

Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.