IGCSE Physics - Moments and Centre of Gravity

Moments

The Moment of a Force

• The moment of a force is the turning effect produced when a force is exerted on an object.
• Examples:
  • A child on a seesaw.
  • Turning a spanner.
  • Opening/closing a door.
  • Using a crane to move building supplies.
  • Using a screwdriver to open a tin of paint.
  • Turning a tap on/off.
  • Picking up a wheelbarrow.
  • Using scissors.
• Forces can cause the rotation of an object about a fixed pivot.
• This rotation can be clockwise or anticlockwise. Consider the hands of a clock when deciding whether the moment is clockwise or anticlockwise.
• A force applied on one side of the pivot will cause the object to rotate.
• A moment is defined as the turning effect of a force about a pivot.
• The size of a moment is defined by the equation: M = F \times d Where:
  • M = moment in newton metres (Nm).
  • F = force in newtons (N).
  • d = perpendicular distance of the force to the pivot in metres (m).
• Forces should be perpendicular to the distance from the pivot.
• On a horizontal beam, forces causing a moment are those directed upwards or downwards.
• Increasing the distance a force is applied from a pivot decreases the force required
• It's more difficult to push open a door right next to the hinge because it requires more force. Pushing at the side furthest from the hinge is easier and requires less force.

Examiner Tips and Tricks

• The moment of a force is measured in newton metres (Nm), but can also be measured in newton centimetres (Ncm) if the distance is measured in cm instead.
• Always convert the distance to metres if the question doesn't ask for a specific unit.

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.
• For a balanced object, moments on both sides of the pivot are equal:
  • clockwise moment = anticlockwise moment
• If a beam moves clockwise when holding the beam about the pivot and applying just one of the forces then the force applied is clockwise.
• Moment = force × distance from a pivot.
• Forces should be perpendicular to the distance from the pivot.
• For a horizontal beam, the forces which will cause a moment are those directed upwards or downwards
• Sum of clockwise moments = Sum of anticlockwise moments
  F2 \times d2 = (F1 \times d1) + (F3 \times d3)

Worked Example

A parent and child are on opposite ends of a seesaw. The parent weighs 690 N and the child weighs 140 N. The adult sits 0.3 m from the pivot.

Calculate the distance the child must sit from the pivot for the seesaw to be balanced.

1. List known quantities:
   • Clockwise force (child), F_{child} = 140 N
   • Anticlockwise force (adult), F_{adult} = 690 N
   • Distance of adult from the pivot, d_{adult} = 0.3 m
2. Write down the relevant equation:
   • Moment = force × distance from pivot
   • Total clockwise moments = Total anticlockwise moments
3. Calculate total clockwise moments:
   • Moment of child (clockwise) = F{child} \times d{child}
   • Moment of child (clockwise) = 140 \times d_{child}
4. Calculate total anticlockwise moments:
   • Moment of adult (anticlockwise) = F{adult} \times d{adult}
   • Moment of adult (anticlockwise) = 690 \times 0.3 = 207 Nm
5. Substitute into the principle of moments equation:
   • Moment of child (clockwise) = Moment of adult (anticlockwise)
   • 140 \times d_{child} = 207
6. Rearrange for the distance of the child from the pivot:
   • d_{child} = \frac{207}{140} = 1.5 m

The child must sit 1.5 m from the pivot to balance the seesaw.

Supporting a Beam

• A light beam can be treated as though it has no mass.
• The supports exert upward forces that balance the downward acting weight of any object placed on the beam.
• F1 and F2 upwards balance the weight of the beam downwards
• As the mass in the diagram is moved from left to right, force F1 will decrease, and force F2 will increase.
• Ensure all distances are in the same units and consider the correct forces as clockwise or anticlockwise.
• If the right-hand support is removed:
  • Force F_2 would be 0.
  • The weight of the object would produce a moment about the left-hand support, causing the beam to pivot clockwise.
• When F_2 is removed, the beam will rotate by the clockwise moment.
• Therefore, force F_1 must supply an anticlockwise moment about the left-hand support, which balances the moment supplied by the object.

Centre of Gravity

• The centre of gravity of an object is defined as the point through which the weight of an object acts.
• For a symmetrical object of uniform density, the centre of gravity is located at the point of symmetry.
• For example, the centre of gravity of a sphere is at the centre.

Finding the Centre of Gravity of Symmetrical Objects

• The centre of gravity of a regular shaped object can be found using symmetry.
• The centre of gravity of an irregular object can be found using suspension.
• The irregular shape is suspended from a pivot and allowed to settle.
• A plumb line (weighted thread) is held next to the pivot, and a pencil is used to draw a vertical line from the pivot (the centre of mass must be somewhere on this line).
• Repeat the process, suspending the shape from two additional points.
• The centre of mass is located at the point where all three lines cross.

Examiner Tips and Tricks

• The centre of gravity is a hypothetical point, so it can lie inside or outside of a body.
• The centre of gravity will constantly shift depending on the shape of a body.
• For example, the human body’s centre of gravity is lower when leaning forward than when standing upright.
• When drawing force diagrams, always draw the weight force as if it were acting from the centre of gravity of the object!