Moments, levers and gears
A moment is the turning effect of a force about a pivot.
Moment formula
$M = Fd$
- $M$ — moment in newton-metres (Nm).
- $F$ — force in newtons.
- $d$ — perpendicular distance from pivot to line of action of force (m).
Principle of moments
For an object in rotational equilibrium (not turning):
Sum of clockwise moments = sum of anticlockwise moments.
Used to balance see-saws, find unknown forces or distances.
✦Worked example— Worked example — see-saw
A see-saw pivots in the middle. A 40 kg child sits 1.5 m left of the pivot. Where must a 30 kg child sit to balance?
- Anticlockwise moment: 40 × 9.8 × 1.5 = 588 Nm (left side).
- Clockwise moment: 30 × 9.8 × d (right side).
- Balance: 588 = 294 × d → d = 2.0 m.
Levers — force multipliers
A lever is a rigid bar pivoted at a fulcrum. A small force at a long distance produces the same moment as a large force at a short distance.
- First class lever: pivot between effort and load (see-saw, scissors).
- Second class: load between pivot and effort (wheelbarrow).
- Third class: effort between pivot and load (tweezers, fishing rod).
A lever doesn't increase total energy — it trades distance for force (and vice versa).
Gears — torque multipliers
Two interlocking cogs of different sizes.
- If the driving gear is smaller than the driven gear: the driven gear turns more slowly but with greater torque. (Gear-up for force.)
- If the driving gear is larger: the driven gear turns faster but with less force. (Gear-up for speed.)
The gear ratio is the ratio of teeth: small to big = force gain.
✦Worked example— Worked example — gears
A 10-tooth gear drives a 30-tooth gear. The smaller turns at 60 rpm with 1 Nm torque. The larger turns at?
- Gear ratio 30:10 = 3:1.
- Larger turns at 60/3 = 20 rpm.
- Torque tripled to 3 Nm.
- (Power constant: small × fast = big × slow.)
⚠Common mistakes
- Using parallel distance instead of perpendicular.
- Forgetting that force × distance must be in newtons × metres.
- Saying levers "create force" — they redistribute it; energy in = energy out (ignoring friction).
- Confusing gear ratio direction.
AI-generated · claude-opus-4-7 · v3-deep-physics