Moments, Couples & Equilibrium

Turning effects of forces, the principle of moments, couples, and centre of mass.

Spec Points Covered
  • Define the moment of a forceThe turning effect of a force about a pivot. Equal to force multiplied by the perpendicular distance from the pivot to the line of action of the force. and calculate it for perpendicular and non-perpendicular forces.
  • State and apply the principle of momentsFor an object in rotational equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.., the sum of clockwise moments about any point equals the sum of anticlockwise moments about the same point. to solve equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. problems.
  • Define a coupleA pair of equal and opposite forces whose lines of action do not coincide, producing a pure turning effect (torque) with no resultant force. and calculate its moment.
  • Locate the centre of mass of uniform regular objects.
  • Explain how the position of the centre of mass affects stability.
  • Distinguish between centre of mass and centre of gravityThe single point at which the entire weight of an object can be considered to act..
Notes
01 A moment is the turning effect of a force Moment 3.4.1.2 → 02 The principle of moments: clockwise equals anticlockwise in equilibrium Principle of moments 3.4.1.2 → 03 A couple is a pair of equal, opposite, parallel forces that produce pure rotation Couple 3.4.1.2 → 04 The centre of mass is the point where weight is considered to act Centre of mass 3.4.1.2 → 05 An object is stable when its centre of mass is above its base 3.4.1.2 → 06 Centre of gravity equals centre of mass in a uniform gravitational field 3.4.1.2 →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
Moment of a force
$$M = F \times d$$
  • Where:
    • $M$ = moment (N m)
    • $F$ = force (N)
    • $d$ = perpendicular distance from pivot (m)
d must be the perpendicular distance to the line of action.
Moment when force is at an angle
$$M = F d \cos \theta$$
  • Where:
    • $M$ = moment (N m)
    • $F$ = applied force (N)
    • $d$ = distance from pivot (m)
    • $θ$ = angle between force direction and perpendicular
Takes the perpendicular component of the distance.
Moment of a couple
$$M = F \times d$$
  • Where:
    • $M$ = moment of couple (N m)
    • $F$ = magnitude of one force (N)
    • $d$ = perpendicular distance between lines of action (m)
The moment of a couple is independent of any pivot point.
Q Retrieval Practice All 8 Questions →
Q1. Define the moment of a forceThe turning effect of a force about a pivot. Equal to force multiplied by the perpendicular distance from the pivot to the line of action of the force..
  • Moment = Force times the perpendicular distance from the pivot to the line of action of the force.
  • Unit: N m.
Q2. State the principle of momentsFor an object in rotational equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.., the sum of clockwise moments about any point equals the sum of anticlockwise moments about the same point..
For a system in equilibrium, the sum of clockwise moments about a point equals the sum of anticlockwise moments about the same point.
Q3. What three conditions must a coupleA pair of equal and opposite forces whose lines of action do not coincide, producing a pure turning effect (torque) with no resultant force. satisfy?
Equal in magnitude, opposite in direction, and separated by a perpendicular distance (lines of action do not coincide).
Q4. Why does a coupleA pair of equal and opposite forces whose lines of action do not coincide, producing a pure turning effect (torque) with no resultant force. produce rotation but no linear accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻².?
  • The two forces are equal and opposite, so the resultant force is zero (no net force means no linear accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻². by Newton's second lawThe resultant force on an object is equal to its rate of change of momentum. For constant mass, F = ma.).
  • But they are separated, so they create a net moment.
Q5. Where is the centre of mass of a uniform rectangular object?
At the geometric centre, where the diagonals cross.