Moments (OCR GCSE Physics A (Gateway))

Forces & Rotation

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

• 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)