4.1.3Dynamics, forces and pressure
Turning Effects of Forces
5 min read 10 parts Lesson 15 of 24 1 quiz
Lesson summary
4.1.3 Turning Effects of Forces — AS PHYSICS 9702 notes: Define a couple and torque and distinguish a couple from the moment of a single force.Couple = a pair of forces that are equal in magnitude, opposite in direction and perpendicular to the distance between them, with lines o…
- The resultant force of a couple is zero
- A couple produces a turning effect only
- Do not use the sum of the two forces
- If the forces are tilted
- A steering wheel of diameter D turned by two hands
- Both moments turn the body the same way
Section 1 of 10Couples
Couples
Couple
Couple a pair of forces that are equal in magnitude, opposite in direction and perpendicular to the distance between them, with lines of action that do not coincide.
The resultant force of a couple is zero
- The resultant force of a couple is zero so by F = ma the centre of mass does not accelerate.
A couple produces a turning effect only
- A couple produces a turning effect only pure rotation.
The forces cannot share the same line of action.
Examples
- Examples turning a tap with finger and thumb, a steering wheel turned with both hands, and a key turned in a lock.
Section 2 of 10Torque of a couple
Torque of a couple
Torque
Torque the moment of a couple.
τ = Fd
- τ is the torque in N m, F is one of the forces in N and d is the perpendicular distance between the forces in m.
Do not use the sum of the two forces
- Do not use the sum of the two forces the torque uses one force, not 2F.
If the forces are tilted
- If the forces are tilted use only the component of the force perpendicular to the line joining them.
A steering wheel of diameter D turned by two hands
- A steering wheel of diameter D turned by two hands torque = FD.
Section 3 of 10Why the torque formula works
Why the torque formula works
Take moments about a pivot at distance x from the nearer force.
Both moments turn the body the same way
- Both moments turn the body the same way their sum is Fx + F(d − x) = Fd.
The result does not depend on the pivot chosen
- The result does not depend on the pivot chosen a couple has the same effect wherever the body rotates.
Section 4 of 10Properties of couples
1
Resultant force zero, resultant moment not zero.
2A couple can only be balanced by another couple
- A couple can only be balanced by another couple of equal size and opposite direction, not by a single force.
3Using one hand on a wheel
- Using one hand on a wheel gives a moment and a net force, so the shaft is pushed sideways;
- a couple avoids this load.
4A compass needle in a uniform magnetic field
- A compass needle in a uniform magnetic field experiences a couple.
Section 5 of 10Moment of a single force and torque of a couple compared
| Feature | Moment of a force | Torque of a couple |
|---|---|---|
| Number of forces | One, about a chosen pivot | Two equal and opposite |
| Resultant force | May be non-zero | Zero |
| Distance used | Perpendicular distance to the pivot | Perpendicular distance between the two forces |
| Depends on pivot | Yes | No, same about every point |
Section 6 of 10Resultant force and resultant moment
1Any set of forces on a rigid body has two effects
- Any set of forces on a rigid body has two effects the resultant force changes how the centre of mass moves and the resultant moment changes the rotation.
2A single force not through the centre of gravity
- A single force not through the centre of gravity causes both.
3A couple isolates the turning effect
- A couple isolates the turning effect with no change in translational motion.
4For a beam hinged at a wall and held by a cable
- For a beam hinged at a wall and held by a cable take moments about the hinge so the unknown hinge force drops out.
Section 7 of 10Finding the torque of a couple
1
Identify the pair of equal and opposite forces.
2
Measure the perpendicular distance between their lines of action.
3
If the forces are tilted, use the component perpendicular to the line joining them.
4
Multiply F by d and give the direction as clockwise or anticlockwise.
5
If a balancing couple is asked for, give one of equal size and opposite direction.
Section 8 of 10More from the specification
1Moment of force in newton metres
- Moment of force in newton metres rotational equilibrium requires clockwise moments to balance anticlockwise moments measured in newton metres.
2Weight
- Gravitational force on a mass.
3Stable
- Returns to its original position when tilted slightly.
4Newton
- Unit of force, kg m s-2.
5Upright
- The same way up as the object
6Symmetry
- Balanced shape about a line or plane.
7Stability
- Resistance to toppling.
8Gravitational field
- Region where mass experiences gravitational force.
9Newton metre
- Unit of moment, Nm.
10Centre of gravity
- Centre of gravity it can move depending on the shape or orientation of the object.
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| Couple | A pair of equal, opposite forces with different lines of action that produces rotation only. |
| Torque of a couple | One of the forces multiplied by the perpendicular distance between the forces. |
| Resultant force | The vector sum of all forces on a body. |
| Resultant moment | The net turning effect of all forces about a point. |
| Line of action | The line along which a force acts. |
| Pure rotation | Turning without any translation of the centre of mass. |
| Newton metre | The unit of moment and torque. |
| Hinge | A pivot that allows a body to turn. |
Section 10 of 10Exam technique
1
Saying a couple has a resultant force — it is zero.
2
Measuring d from one force to the pivot instead of between the two lines of action.
3
Giving the torque in joules — it is N m.
4
Using 2F in the torque formula.
5
Thinking a couple can be balanced by a single force.