Moments

What a moment is

• A moment is the turning effect of a force about a fixed point called the pivot
• A force does not always make an object change its straight-line motion; if the object is free to rotate about a hinge or axle, the force instead makes it spin
• Common everyday moments include:
  • the handle of a door rotating about its hinges
  • a spanner loosening a bolt
  • a child on one end of a see-saw lifting another child at the far end
  • a screwdriver prising open a tin lid
  • a tap being twisted on or off
  • a wheelbarrow being tipped up to be wheeled
  • the blades of a pair of scissors closing about the rivet
• The rotation may be clockwise or anticlockwise, depending on which side of the pivot the force is applied and which way it points

The equation

M = F × d

• where:
  • M = moment of the force (newton metres, N m)
  • F = force applied (N)
  • d = perpendicular distance from the pivot to the line of action of the force (m)
• The unit follows from the equation: newton × metre → newton metre (N m). If the lever arm is given in centimetres, the moment can equally be quoted in N cm; convert to metres unless the question asks otherwise

Why the distance must be perpendicular

• The lever arm d is the shortest distance from the pivot to the line along which the force acts, measured at right angles to that line
• A force pointing straight at the pivot has zero perpendicular distance, so it produces no moment no matter how large it is; it simply tries to push the pivot itself
• For a beam lying flat, only the vertical forces (those pointing straight up or straight down) turn it about a pivot on the beam; a force directed along the length of the beam contributes no moment at all

Long lever arms make life easier

• For a fixed pivot, a longer lever arm reduces the force you must apply to get the same moment
• Real-life consequences:
  • A door is far easier to push open at the handle (far from the hinge) than near the hinge itself; the same moment comes from a much smaller hand force when d is large
  • A wheel nut wrench with a long extension bar makes seized nuts shift that a stubby spanner cannot
  • A short crowbar prises open a crate with a much smaller hand force than fingers alone