Library / Foundations: Physics / FPH-17
Foundations: Physics
Moment of a force
Turning effect of a force about a pivot.
- Ref
- FPH-17
- Rev
- v1
- Field
- Foundations: Physics
- Result
- M [N·m]
Use the shortest distance from the pivot to the force’s line of action. In rotational equilibrium, clockwise and anticlockwise moments balance.
A force has more turning effect the further from the pivot it acts.
Calculator
N·m
N
m
- Force needed at 2× the distance60 N
- Moment in kN·m0.054 kN·m
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
Moment (N·m) current value 54 N·m
FForceKey driver
0.452,250
dPerpendicular distance
1.2600
- A longer spanner lets you apply the same turning effect with less force.
- A beam balances when clockwise and anticlockwise moments are equal.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (N·m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| F Force | 1 to 5,000 N | 0.45 | 2,250 | 2,250 | +10% | +10 % |
| d Perpendicular distance | 0.01 to 5 m | 1.2 | 600 | 598.8 | +10% | +10 % |
Sweep of Perpendicular distance
| Perpendicular distance (m) | Moment (N·m) |
|---|---|
| 0.01 | 1.2 |
| 0.02175 | 2.609 |
| 0.04729 | 5.674 |
| 0.1028 | 12.34 |
| 0.2236 | 26.83 |
| 0.4862 | 58.35 |
| 1.057 | 126.9 |
| 2.299 | 275.9 |
| 5 | 600 |
Sweep one variable
Moment (N·m)Hover, touch, or use the arrow keys on the chart
Variables and how each one contributes
M
Moment
What the equation gives you. Everything else feeds it.
F
Force
Applied force. Directly proportional.
d
Perpendicular distance
Distance from pivot to force line, at right angles. Directly proportional.
Worked example with the values above
- Force 120 N at 0.45 m.
- Multiply them.
- M = 54 N·m.
Assumptions and limits
- Distance measured perpendicular to the force.
- Forces in the same plane.
Common mistakes
- Using the distance along the arm rather than the perpendicular distance.
- Mixing cm and m.
Statistics and uncertainty
The perpendicular distance is often estimated; a 5% error in distance gives 5% error in the moment.
Where it is used
- Lever, crane and balance problems.
- Tightening torques.
Maths you need
- Force: newtons
- Distance: perpendicular