Moments (OCR Gateway GCSE Physics)

Rotation

• As well as causing objects to speed up, slow down, change direction and deform, forces can also cause objects to rotate
  • A system of forces can also do this

• An example of a rotation caused by a force is on one side of a pivot (a fixed point that the object can rotate around)
  • This rotation can be clockwise or anticlockwise

The force will cause the object to rotate clockwise about the pivot

• More examples of rotation caused by a force are:
  • A child on a see-saw
  • Turning the handle of a spanner
  • A door opening and closing

• If two forces act on an object without passing through the same point, then the object can still rotate
  • If the forces are equal and opposite, this is known as a couple

The above forces are balanced, but will still cause the object to rotate clockwise as they don’t act through a common point

Calculating Moments

• 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 × 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)

The moment depends on the force and perpendicular distance to the pivot

• This is why, for example, the door handle is placed on the opposite side to the hinge
  • This means for a given force, the perpendicular distance from the pivot (the hinge) is larger
  • This creates a larger moment (turning effect) to make it easier to open the door

• Opening a door with a handle close to the pivot would be much harder, and would require a lot more force

• 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 the pivot
• The forces should be perpendicular to the distance from the pivot
  • For example, on a horizontal beam, the forces that will cause a moment are those directed upwards or downwards

Moments on a balanced beam

• In the above diagram:
  • Force F₂ is supplying a clockwise moment;
  • Forces F₁ and F₃ are supplying anticlockwise moments

• Due to the principle of moments, if the beam is balanced

Total clockwise moments = Total anticlockwise moments

• Hence:

F₂ × d₂ = (F₁ × d₁) + (F₃ × d₃)

Step 1: List the know 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

Step 2: Write down the relevant equation

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

Moment_child = F_child × d_child = 140 × d_child

Step 4: Calculate the total anticlockwise moments

• • The anticlockwise moment is from the adult

Moment_adult = F_adult × d_adult = 690 × 0.3 = 207 Nm

Step 5: Substitute into the principle of moments equation

140 × d_child = 207

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

d_child = 207 ÷ 140 = 1.48 m