The shape of the lesson
By the end of the lesson, learners can
- Distance matters as much as force: Slide the loads along the beam and change their weights.
- Moment, couple, torque: The distance in a moment is always the perpendicular distance from the pivot to the line of action.
- Finding the centre of gravity.
- Moment: force × perpendicular distance from the pivot.
- Force at an angle: moment = F r sinθ.
- Couple: torque = one force × the separation.
One picture every idea returns to
The moment of a force about a point is the force multiplied by the perpendicular distance from the point to the line of action of the force: moment = F × d, measured in N m. The centre of gravity is the single point at which the entire weight of a body appears to act. A couple is a pair of equal, antiparallel forces whose only effect is to turn; its torque is one force × the perpendicular separation.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Force times distance, sideways.. A force can do more than push a body along: applied off-centre, it turns it. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 13 min | Teach and check: Distance matters as much as force | Slide the loads along the beam and change their weights. Project tab 1 of the lab (Turning effects of forces) and let a student drive it while the class predicts. | Whole class, then pairs |
| 13 to 21 min | Teach and check: Moment, couple, torque | The distance in a moment is always the perpendicular distance from the pivot to the line of action. | Pairs |
| 21 to 30 min | Teach and check: Finding the centre of gravity | Finding the centre of gravity. | Frayer Model |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 15 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Finding the centre of gravity, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Frayer Model
Pairs fill a four-box grid for the key term: definition, characteristics, examples and non-examples. The non-examples box is where the misconceptions surface, so give it the most time.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Use the perpendicular distance, not the distance along the force or the slanted distance to the pivot. | If a force acts at an angle, the moment is F r sinθ, not F r. A second trap: a couple has no resultant force, so do not look for one; its torque is the force times the separation of the two lines of action, and you do not multiply by two even though there are two forces. |
Turning effects of forces: worksheet
6 questions, 15 marks. Written in the style of the papers; no past paper question is reproduced.
Define the moment of a force about a point, and give its SI unit.
A door handle is 0.80 m from the hinge. A person pushes with 25 N perpendicular to the door at the handle. Find the moment about the hinge.
A force of 60 N is applied at the end of a 0.50 m lever, at an angle of 40° to the lever. Find the moment of the force about the other end.
A steering wheel is turned by two forces of 8.0 N applied at opposite ends of a diameter of 0.36 m, forming a couple. Find the torque of the couple.
Describe an experiment to find the centre of gravity of an irregular flat lamina using a plumb line.
A uniform beam of weight 12 N and length 2.0 m is pivoted 0.50 m from its left end. Find the moment of the beam's weight about the pivot, and state whether it acts clockwise or anticlockwise about the pivot.
Answer key and marking notes
- The moment is the force multiplied by the perpendicular distance from the point to the line of action of the force. ✓
- Its unit is the newton metre (N m). ✓
Moment = F × d = 25 × 0.80 = 20 N m. ✓
- Perpendicular distance = 0.50 sin 40° = 0.50 × 0.643 = 0.321 m. ✓
- Moment = 60 × 0.321 = 19 N m. (Equivalently 60 × 0.50 × sin 40°.) ✓
- Torque of a couple = one force × the separation = 8.0 × 0.36 = 2.9 N m. ✓
- (Do not multiply by two; the formula already accounts for both forces.) ✓
- Hang the lamina freely from a pin through one hole and let it settle; hang a plumb line from the same pin and mark the vertical line. ✓
- Repeat from a second hole to get another line. ✓
- The centre of gravity is the point where the two lines cross. ✓
- The weight acts at the centre of gravity, the midpoint, which is 1.0 m from the left end. ✓
- This is 1.0 − 0.50 = 0.50 m to the right of the pivot. ✓
- Moment = 12 × 0.50 = 6.0 N m, acting clockwise (the heavy side is to the right of the pivot). ✓
17 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
The moment of a force about a point is the force multiplied by the:
- Aperpendicular distance from the point to the line of action
- Bdistance the force moves
- Ctime the force acts
- Dmass of the body
The SI unit of the moment of a force is the:
- Anewton
- Bjoule
- Cnewton metre
- Dpascal
A force of 15 N acts at a perpendicular distance of 0.40 m from a pivot. The moment is:
- A37.5 N m
- B6.0 N m
- C0.6 N m
- D15.4 N m
A force of 30 N acts perpendicular to a spanner at 0.60 m from the bolt. The moment about the bolt is:
- A50 N m
- B0.5 N m
- C30 N m
- D18 N m
The centre of gravity of a body is the point where:
- Aits whole weight appears to act
- Bits volume is largest
- Cthe upthrust acts
- Dit always balances on any pivot
A couple consists of two equal and opposite parallel forces not in the same line. It produces:
- Aa resultant force with no turning effect
- Bno effect at all
- Ca turning effect with no resultant force
- Dlinear acceleration
Two 5.0 N forces form a couple acting along lines 0.40 m apart. The torque of the couple is:
- A4.0 N m
- B2.0 N m
- C1.0 N m
- D12.5 N m
Why is it easier to loosen a bolt with a long spanner than a short one?
- Athe longer spanner reduces the force needed to zero
- Ba longer spanner weighs more
- Cthe bolt becomes weaker
- Dthe longer spanner gives a larger moment for the same force
A force of 10 N acts at the end of a 0.50 m rod, at 30 degrees to the rod. The moment about the other end is:
- A2.5 N m
- B5.0 N m
- C4.3 N m
- D1.4 N m
For a uniform beam, the centre of gravity is located:
- Aat one end
- Bone third from an end
- Cat its midpoint
- Dwhere it is supported
A pivoted rule has a 3.0 N weight 40 cm from the pivot on one side. A weight on the other side balances it at 20 cm. That weight is:
- A1.5 N
- B6.0 N
- C3.0 N
- D12 N
To increase the moment of a fixed force about a pivot, you should:
- Aapply it closer to the pivot
- Bapply it along the line through the pivot
- Creduce the distance to zero
- Dapply it at a greater perpendicular distance
An object is more stable when it has:
- Aa lower centre of gravity and a wider base
- Ba higher centre of gravity
- Ca narrower base
- Da larger weight only
A door handle is placed far from the hinges rather than near them because this:
- Areduces the weight of the door
- Blooks better only
- Cincreases the moment for a given push
- Dincreases the friction
A uniform beam of weight 20 N and length 2.0 m is pivoted 0.50 m from one end. The moment of its weight about the pivot is:
- A20 N m
- B10 N m
- C5.0 N m
- D40 N m
The torque of a given couple is the same:
- Aonly about the midpoint between the forces
- Bonly about one of the forces
- Conly at the centre of gravity
- Dabout any point in its plane
A see-saw balances a 600 N adult 0.50 m from the pivot with a 200 N child. The child must sit at a distance of:
- A1.5 m
- B0.17 m
- C3.0 m
- D1.0 m
Quiz key
Moment = force x perpendicular distance from the point to the line of action of the force.
Moment = N x m = newton metre (N m). It is not the joule, although the units look alike.
Moment = 15 x 0.40 = 6.0 N m.
Moment = 30 x 0.60 = 18 N m.
The centre of gravity is the single point at which the entire weight of the body can be taken to act.
The two forces cancel as a resultant but, being offset, give a pure turning effect (a torque).
Torque of a couple = one force x the separation = 5.0 x 0.40 = 2.0 N m.
A longer spanner means a greater perpendicular distance, so the same force gives a larger moment.
Moment = F r sin theta = 10 x 0.50 x sin 30 = 10 x 0.50 x 0.5 = 2.5 N m.
A uniform beam has its centre of gravity at its geometric centre, the midpoint.
Balance: 3.0 x 40 = W x 20, so W = 120 / 20 = 6.0 N.
Moment = F x perpendicular distance, so a greater perpendicular distance gives a larger moment.
A lower centre of gravity and wider base let the body tilt further before its weight line falls outside the base, so it is more stable.
Placing the handle far from the hinge gives a large perpendicular distance, so a modest push gives a large moment to open the door.
The centre of gravity is at 1.0 m from the end, which is 0.50 m from the pivot. Moment = 20 x 0.50 = 10 N m.
A couple has the same torque about every point in its plane, because it has no resultant force.
600 x 0.50 = 200 x d, so d = 300 / 200 = 1.5 m.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.