Lesson summary
4.1.2 Moments — AS PHYSICS 9702 notes: Define the moment of a force and calculate it using the perpendicular distance from the pivot.Moment = the turning effect of a force about a pivot.moment = Fd — F is the force in N and d is the perpendicular distance from the pivot to the li…
- What the symbols mean
- The unit is the newton metre (N m)
- The moment depends on two things
- A force at angle θ to a spanner of length L
- Equivalent view
- The component along the lever, F cos θ
Section 1 of 9What a moment is
What a moment is
Moment
Moment the turning effect of a force about a pivot.
moment = Fd
- F is the force in N and d is the perpendicular distance from the pivot to the line of action of the force, in m.What the symbols mean: moment (N m) · F = force (N) · d = perpendicular distance from the pivot to the line of the force (m)
The unit is the newton metre (N m)
- The unit is the newton metre (N m) not the same as the joule, because no energy is transferred.
The moment depends on two things
- The moment depends on two things the size of the force and how far from the pivot it acts.
Moments are described as clockwise or anticlockwise.
Section 2 of 9Perpendicular distance
Perpendicular distance
The distance in the formula must be at right angles to the line of action of the force.
A force at angle θ to a spanner of length L
- A force at angle θ to a spanner of length L d = L sin θ, so moment = FL sin θ.
Equivalent view
- Equivalent view moment = L × the component of force perpendicular to the lever, F sin θ.
The component along the lever, F cos θ
- The component along the lever, F cos θ has no turning effect because its line of action passes through the pivot.
A force whose line of action passes through the pivot has zero moment
- A force whose line of action passes through the pivot has zero moment however big it is.
Section 3 of 9Choosing a pivot and direction
Choosing a pivot and direction
The pivot can be any point.
Choose a point where an unknown force acts
- Choose a point where an unknown force acts that force has zero moment and drops out of the equation.
Choose one turning direction as positive
- Choose one turning direction as positive or keep clockwise and anticlockwise moments in separate groups.
Resultant moment
Resultant moment the sum of clockwise moments minus the sum of anticlockwise moments.
If the resultant moment is zero
- If the resultant moment is zero the body does not start to rotate.
Section 4 of 9Everyday applications
Everyday applications
A long spanner
- A long spanner gives the same moment with a smaller force because d is larger.
Door handles are placed far from the hinges
- Door handles are placed far from the hinges for the same reason.
A wheelbarrow, crowbar and scissors are levers
- A wheelbarrow, crowbar and scissors are levers a small force far from the pivot balances a large force near it.
In a lever Fe de
Fl dl
- the effort force Fe at distance de balances the load force Fl at distance dl.
Required force is inversely proportional to the distance
- Required force is inversely proportional to the distance a 0.50 m wrench needs half the force of a 0.25 m wrench for the same torque.
Section 5 of 9Weights in moment calculations
1The weight of a uniform beam or lamina
- The weight of a uniform beam or lamina acts at its centre of gravity (see 4.1.1).
2Use weight in newtons
- Use weight in newtons not mass in kg.
3Convert distances to metres
- Convert distances to metres and work with extra significant figures, rounding at the end.
4Draw a diagram of all the forces
- Draw a diagram of all the forces not all of them give a turning effect.
Section 6 of 9Link to equilibrium
1When a body is in rotational equilibrium
- When a body is in rotational equilibrium the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about the same point (see 4.2).
2First evaluate a single moment correctly
- First evaluate a single moment correctly check the angle and identify the perpendicular distance.
Section 7 of 9More from the specification
Couple
- A pair of equal opposite forces with different lines of action.
Stable
- Returns to its original position when tilted slightly.
Upright
- The same way up as the object
Symmetry
- Balanced shape about a line or plane.
Stability
- Resistance to toppling.
Gravitational field
- Region where mass experiences gravitational force.
Line of action
- Line of action the straight line along the direction of a force, passing through its point of application.
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Moment | The turning effect of a force about a pivot, force times perpendicular distance. |
| Pivot | The point about which a body turns. |
| Line of action | The line along which a force acts. |
| Perpendicular distance | The shortest distance from the pivot to the line of action. |
| Clockwise moment | A moment that turns a body clockwise. |
| Anticlockwise moment | A moment that turns a body anticlockwise. |
| Lever | A rigid bar that turns about a pivot to balance a load with an effort. |
| Newton metre | The unit of moment, N m. |
Section 9 of 9Exam technique
1
Measuring the distance to the point where the force is applied rather than the perpendicular distance from the line of action.
2
Using sin θ and cos θ the wrong way round — check which angle is between the force and the lever arm.
3
Writing the unit of moment as joules — it is N m.
4
Using mass in kg instead of weight in N.