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Theme A — Space, Time and Motion

A.4.1 Torque and Couples — IB Physics HL Revision Notes & Topical Questions

5 min read 8 parts Lesson 43 of 63 1 quiz

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A.4.1 Torque and Couples — IB PHYSICS HL notes: Define the moment of a force, couples and torque and calculate them for perpendicular and non-perpendicular forces.Moment = the turning effect of a force about a pivot.Moment (N m) = force × perpendicular distance from the pivot.If …

  • A moment is the effect of the force at a distance
  • For perpendicular forces (θ
  • The torque is maximum when the force acts perpendicular to the lever
  • Moment of a couple
  • A couple has zero resultant force
  • It has a net torque

Part 1 of 6Moment of a force

1Moment
Moment the turning effect of a force about a pivot.
2Moment (N m)
Moment (N m) force × perpendicular distance from the pivot.
3
If the force is not perpendicular to the distance, resolve it in the perpendicular direction with trigonometry.
4A moment is the effect of the force at a distance
  • A moment is the effect of the force at a distance not the force itself.

Part 2 of 6Torque

Torque
Torque
Torque the change in rotational motion due to a turning force — another term for moment.
τ
Fr sin θ
  • F is the applied force, r the distance from the axis and θ the angle between them.
For perpendicular forces (θ
90°) the torque is τ = Fr.
The torque is maximum when the force acts perpendicular to the lever
  • The torque is maximum when the force acts perpendicular to the lever e.g. a wrench or a pedal.
  • At θ = 180° sin θ = 0, so a downward push at the bottom of a pedal gives no torque.
Identify the force magnitude and the perpendicular distance along the line of action.

Part 3 of 6Couples

A couple
A couple a pair of equal and opposite coplanar forces that act to produce rotation only.
Conditions.
  • Equal in magnitude.
  • Opposite in direction.
  • Perpendicular to the distance between them and not sharing a line of action.
Moment of a couple
Moment of a couple force × perpendicular distance between the lines of action.
The moment of a couple does not depend on any pivot.

Part 4 of 6Torque of a couple

1A couple has zero resultant force
  • A couple has zero resultant force so no linear acceleration and the body is in translational equilibrium.
2It has a net torque
  • It has a net torque which gives angular acceleration.
3Net torque of a couple
Net torque of a couple sum of the moments of each force.
  • For a steering wheel of radius r with θ = 90°: τ = Fr + Fr = 2Fr.
  • A ruler of length 0.3 m with 4 N at each end has torque 4 × 0.3 = 1.2 N m.
4
The wheel rotates in place and its angular speed increases.

Part 5 of 6Terminology

1Moment is not a "turning force"
  • Moment is not a "turning force" the force is only part of the moment.
2Torque is another term for moment
  • Torque is another term for moment and in mechanics it also describes the moment of a couple.
3Torque is a vector
  • Torque is a vector at this level only clockwise or anticlockwise matters.
4A resultant torque causes angular acceleration
  • A resultant torque causes angular acceleration the rotational analogue of a resultant force causing linear acceleration.

Part 6 of 6More from the specification

More from the specification
Rotational torque acting on a mechanical system
  • Rotational torque acting on a mechanical system applying a force couple produces pure angular acceleration without translating the centre of mass of the system.
Torque
  • Torque the turning effect of a force, equal to force times perpendicular distance from the pivot.
Couple
  • Couple two equal and opposite parallel forces that produce rotation without a net force.
Equilibrium
  • Equilibrium there is no resultant force and no resultant torque, so clockwise moments equal anticlockwise moments.
Moment of inertia
  • Moment of inertia a body's resistance to angular acceleration, so torque equals I times angular acceleration.
Angular quantities
  • Angular quantities angular displacement, velocity and acceleration are rotational analogues of linear quantities.
Kinetic energy
  • K = ½mv2, energy of motion.
Velocity
  • Rate of change of displacement.
Inertia
  • Resistance of an object to changes in its motion.
Displacement
  • Change in position.
Newton
  • Unit of force, kg m s-2.
Impulse
  • J = FΔt = Δp.
    What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = change in momentum (kg m s−1); FΔt is the impulse (N s)
Constant
  • Not changing.

Key terms

TermMeaning
MomentForce multiplied by perpendicular distance from the pivot.
TorqueTurning effect of a force, Fr sin θ.
CouplePair of equal and opposite coplanar forces producing rotation only.
PivotPoint or axis about which rotation occurs.
Line of actionLine along which a force acts.
Translational equilibriumState of zero resultant force.

Avoid these mistakes

1
Using the full length instead of the perpendicular distance to the line of action.
2
Thinking a couple produces a resultant force — the resultant force is zero.
3
Forgetting sin θ when the force is not perpendicular.
4
Letting the two forces of a couple share a line of action.
5
Treating the moment of a couple as depending on the pivot.

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