Moments, levers and gears

• Turning forces are found in many everyday situations and are essential for machines to function
• Levers and gears make use of turning forces to provide an advantage
• A moment is the turning effect of a force, acting about a point in a clockwise or anticlockwise direction
• The pivot, also known as the fulcrum, is the point around which something can rotate or turn
• The magnitude of a moment can be calculated using the equation: moment of a force = force × distance (M = F × d)
• Moment (M) is measured in newton-metres (Nm)
• Force (F) is measured in newtons (N)
• Distance (d) is measured in metres (m)
• The distance (d) in the moment equation is the perpendicular distance from the pivot to the line of action of the force
• Turning forces are found in many everyday situations and are essential for machines to function
• Levers and gears make use of turning forces to provide an advantage
• If an object is balanced, the total clockwise moment about a pivot is equal to the total anticlockwise moment about that pivot
• For a balanced object, you can calculate the size of a force or the perpendicular distance of a force from the pivot
• Levers and gears make use of turning forces to provide an advantage
• Levers consist of a pivot, effort, and load
• Examples of different types of levers:

  • Effort - pivot - load: see-saw, crowbar, scissors
  • Pivot - load - effort: wheelbarrow, nutcracker
  • Pivot - effort - load: tweezers, cooking tongs
• A simple lever is a solid beam laid across a pivot, where effort applied to one end rotates the opposite end about the pivot in the same direction, lifting the load
• Levers act as force multipliers, allowing a larger force to act upon the load than is supplied by the effort
• The longer the lever and the further the effort acts from the pivot, the greater the force on the load will be
• Example: A solid beam 0.5 m long laid across a pivot with the pivot 0.1 m from the end. Calculate the heaviest load that could be lifted using a force of 500 N:

  • Calculate the moment due to the 500 N force
  • Calculate the greatest distance from the pivot: 0.5 - 0.1 = 0.4
  • Calculate the moment: M = 500 x 0.4 = 200 Nm
  • Calculate the maximum force 0.1 m from the pivot: F = M / d = 200 / 0.1 = 2000 N
  • The heaviest load that could be lifted is 2,000 N, making it a 4× force multiplier
• Gears are toothed wheels that rotate on an axle or shaft
• Gears are used with other gears to turn axles at different speeds
• As one gear turns, the other gear must also turn in the same direction
• The forces acting on the teeth of gears are identical, but their moments can be different
• If a driven gear is larger, it will rotate more slowly but with a greater moment (low gear ratio)
• If a driven gear is smaller, it will rotate more quickly but with a smaller moment (high gear ratio)
• Turning a gear that has double the radius doubles the turning effect - it is a 2× force multiplier
• Example:

  • Gear with a radius of 0.1 m is turned by a gear with a radius of 0.05 m
  • Moment of the smaller gear is 20 Nm
  • Calculate the moment of the larger gear:
  • Force on the teeth of the smaller gear is 400 N
  • Moment of the larger gear is 40 Nm