๐ In-Depth Theory
Moments
A MOMENT is the turning effect of a force about a pivot.
EQUATION:
Moment = Force ร perpendicular distance from the pivot
M = F ร d
M = moment (newton-metres, Nยทm)
F = force (newtons, N)
d = perpendicular distance from line of action of force to pivot (metres, m)
Direction:
CLOCKWISE moment: force tends to turn the object clockwise.
ANTICLOCKWISE moment: force tends to turn the object anticlockwise.
EXAMPLE:
A 50 N force applied 0.4 m from a pivot:
M = 50 ร 0.4 = 20 Nยทm
LARGER MOMENT can be achieved by:
Increasing the FORCE, OR
Increasing the DISTANCE from the pivot.
This is why door handles are at the edge, not the hinge side.
Principle of Moments and Levers
PRINCIPLE OF MOMENTS (equilibrium condition):
For an object in equilibrium, total clockwise moments = total anticlockwise moments about any pivot.
ฮฃ(F ร d) clockwise = ฮฃ(F ร d) anticlockwise
EXAMPLE โ balanced seesaw:
Child A (600 N) sits 1.5 m from pivot.
Clockwise moment = 600 ร 1.5 = 900 Nยทm
Child B must produce 900 Nยทm anticlockwise.
If Child B weighs 450 N: distance = 900 รท 450 = 2 m from pivot.
LEVERS as FORCE MULTIPLIERS:
A lever is a rigid rod that pivots about a fulcrum (pivot).
Small input force ร long distance = large output force ร short distance.
EXAMPLES: wheelbarrow, crowbar, scissors, tweezers, nutcracker, fishing rod.
Different CLASSES of levers have pivot, effort and load in different positions:
Class 1: pivot between effort and load (seesaw, crowbar).
Class 2: load between pivot and effort (wheelbarrow, nutcracker).
Class 3: effort between pivot and load (tweezers, fishing rod).
Gears
GEARS are toothed wheels that transmit force and rotation.
How gears work:
Meshed gears rotate in OPPOSITE DIRECTIONS.
The teeth interlock โ no slipping.
GEAR RATIO:
Gear ratio = number of teeth on driven gear รท number of teeth on driving gear
LARGE GEAR driven by SMALL GEAR:
Output gear rotates SLOWER but with MORE FORCE (torque).
Used to increase turning force โ e.g. low gear in a car for acceleration.
SMALL GEAR driven by LARGE GEAR:
Output gear rotates FASTER but with LESS FORCE.
Used to increase speed โ e.g. high gear in a car at speed.
GEARS AS FORCE MULTIPLIERS:
Like levers, gears convert a small force over a large rotation into a large force over a small rotation (or vice versa).
Energy is conserved โ work done is the same (ignoring friction).
APPLICATIONS:
Bicycle gears โ change between speed and force.
Car gearbox โ match engine output to driving conditions.
Clocks โ precise speed reduction from mainspring to hour hand.
Wind turbines โ gearbox speeds up slow blade rotation for the generator.
โ ๏ธ Common Mistake
Distance in moments must be the PERPENDICULAR distance from the line of action of the force to the pivot โ not the distance along the lever. For the principle of moments, the object must be in equilibrium (balanced and not rotating).