OCR Specification focus:
‘Define moment of a force and apply moment = F x perpendicular distance from pivot.’
Understanding moments of a force is essential in analysing the rotational effects of forces in physical systems. This concept explains how forces cause objects to turn or balance around a point or axis.
What is a Moment of a Force
A moment of a force describes the turning effect a force produces about a specific point or pivot. It plays a crucial role in maintaining or disrupting equilibrium in mechanical systems.
Moment of a force: The product of the force and the perpendicular distance from the pivot (or axis of rotation) to the line of action of the force.
When a force acts on an object at some distance from a pivot, it tends to rotate the object. The greater the distance or the larger the force, the greater the turning effect. Moments are vector quantities, having both magnitude and direction (clockwise or anticlockwise).
Panels compare torque when pushing a door at different distances from the hinges, with different force magnitudes, and at different angles. Maximum turning effect occurs when the push is perpendicular and far from the hinge; smaller force, smaller distance, or a non-perpendicular push reduces the moment. This aligns directly with moment = F × d and the need for the perpendicular component of the force. Source
The Moment Equation
EQUATION
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Moment (M) = Force (F) × Perpendicular distance from pivot (d)
M = F × d
M = Moment of the force (newton metre, N m)
F = Force applied (newton, N)
d = Perpendicular distance from the pivot to the line of action of the force (metre, m)
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The direction of a moment determines whether it is clockwise or anticlockwise. Conventionally, clockwise moments are considered positive and anticlockwise moments negative, or vice versa, depending on the context.
Understanding Perpendicular Distance
The perpendicular distance is the shortest distance from the pivot point to the line of action of the force. Only this perpendicular component contributes to rotation.
A force F acts at a point, with a clearly marked line of action. The perpendicular distance from the pivot to this line is the lever arm d, the quantity used in moment = F × d. This diagram focuses only on the geometric relationship required by the OCR definition. Source
If a force acts directly through the pivot, the perpendicular distance is zero, and no moment is produced.
If the force is not perpendicular, only the perpendicular component contributes to the turning effect.
This concept is crucial for interpreting and calculating the effective rotational influence of forces in various geometries.
Clockwise and Anticlockwise Moments
Moments act in one of two directions:
Clockwise moments turn objects in the direction of a clock’s hands.
Anticlockwise moments turn objects in the opposite direction.
In a balanced system, these moments counteract each other. Engineers and physicists use the distinction between directions to analyse rotational equilibrium in static structures.
Significance of Moments in Physics
Moments are central to the study of equilibrium, levers, balance, and rotational dynamics. They allow prediction of how forces interact to produce motion or maintain stability.
Key principles:
A single force acting on a body produces both translational and rotational effects.
If several forces act, the resultant moment about a point is the sum of all individual moments, considering their direction.
When moments are balanced, the object is in rotational equilibrium.
Conditions for Zero Moment
A moment becomes zero under the following conditions:
The force acts through the pivot.
The distance from the pivot to the line of action of the force is zero.
Two equal and opposite forces act through the same line of action, cancelling rotation.
Recognising when moments cancel is essential for determining equilibrium conditions.
Units and Measurement
The SI unit of moment is the newton metre (N m).
1 N m corresponds to a 1 N force acting 1 m from a pivot.
Moments can be measured directly using torque wrenches or calculated by measuring forces and distances.
The concept links closely with torque, particularly in rotational motion, where torque is the vector equivalent of a moment.
Moment as a Vector Quantity
Moments are vector quantities because they depend on both magnitude and direction. The axis of rotation determines the moment vector’s direction, following the right-hand rule:
Curl the fingers in the direction of rotation.
The thumb points in the direction of the moment vector.
This representation helps in three-dimensional systems where multiple forces act on different planes.
Practical Applications of Moments
Moments explain everyday mechanical operations:
Levers (e.g., seesaws, crowbars) rely on moments for mechanical advantage.
A first-class lever is shown with forces F₁ and F₂ acting at distances r₁ and r₂ from the pivot P. For equilibrium, the clockwise and anticlockwise moments balance, i.e. F₁r₁ = F₂r₂. The figure contains only the essential labels needed for OCR A-Level students. Source
Door handles are placed far from hinges to increase the perpendicular distance, enhancing turning effect.
Spanners and wrenches apply the same principle — greater length gives a greater moment for the same force.
Balancing beams and scales use equal and opposite moments to achieve equilibrium.
These examples illustrate how understanding moments enables efficient design and operation of tools and systems.
Analysing Systems with Moments
When multiple forces act on a body, determine the resultant moment about a chosen pivot:
Identify all forces acting on the object.
Measure the perpendicular distance from the pivot to each force’s line of action.
Calculate each moment (M = F × d).
Assign positive or negative signs depending on direction.
Sum all moments to find the net (resultant) moment.
If the sum of clockwise moments equals the sum of anticlockwise moments, the body is in rotational equilibrium.
Factors Influencing the Magnitude of a Moment
The size of a moment depends on two factors:
Magnitude of the force (F): A greater force produces a larger moment for the same distance.
Perpendicular distance (d): Increasing the distance increases the moment for a constant force.
Designers exploit these relationships to optimise tools, ensuring maximum efficiency with minimal effort.
Graphical Representation
Moments can be represented using force diagrams or vector notation. In diagrams:
The pivot point is clearly marked.
Lines of action of forces are drawn.
Perpendicular distances are indicated to calculate moments geometrically.
Graphical methods aid in visualising how forces combine to cause or prevent rotation, especially in complex systems.
Summary of Core Learning for OCR A-Level Physics
Students must:
Define a moment of a force as the product of force and perpendicular distance from the pivot.
Apply the moment equation (moment = F × perpendicular distance from pivot) to solve rotational problems.
Identify clockwise and anticlockwise moments in equilibrium scenarios.
Understand how the line of action and perpendicular distance determine the rotational effect.
Use appropriate units (N m) and vector notation to express results clearly.
Through these concepts, learners gain foundational understanding for subsequent topics on couples, torque, and equilibrium of forces and moments.
FAQ
A moment and torque both describe turning effects of a force, but they are often used in slightly different contexts.
Moment usually refers to the turning effect of a force in static systems, such as beams, levers, or structures.
Torque is more commonly used when discussing rotating machinery or systems involving angular acceleration, such as engines or wheels.
Both share the same unit, the newton metre (N m), and are calculated using the same principle: force multiplied by perpendicular distance from the pivot or axis.
Only the perpendicular component of a force contributes to rotation. If a force acts at an angle, part of it pulls sideways rather than turning the object.
To isolate the effective turning influence, we use the shortest distance from the pivot to the force’s line of action.
If a force is not perpendicular, the moment can be found using:
Moment = F × d × sin(θ),
where θ is the angle between the force and the lever arm.
Yes. In three-dimensional systems, moments are treated as vectors that act about an axis, not just a point.
The direction of the moment vector is determined using the right-hand rule: curl your fingers in the direction of rotation; your thumb points along the moment’s direction.
Complex 3D systems often involve multiple moments acting in different planes, which are combined using vector addition.
This vector treatment becomes particularly important in engineering mechanics and rotational motion studies.
You can verify the principle using a metre rule balanced on a pivot:
Place the pivot at the centre of the rule.
Hang known weights at measured distances on either side.
Adjust the weights or distances until the rule is level (in equilibrium).
When balanced, the sum of clockwise moments equals the sum of anticlockwise moments.
Measurements can be repeated with different weight combinations to demonstrate the proportionality between force and distance.
An object may not rotate if:
The line of action of the applied force passes directly through the pivot.
The moment of another force cancels it, producing rotational equilibrium.
Additionally, friction or mechanical constraints can prevent rotation even when moments exist.
In such cases, although the moment is acting, the system resists motion due to equal and opposite moments or static frictional torque, maintaining balance without rotation.
Practice Questions
Question 1 (2 marks)
A horizontal force of 12 N acts on a spanner that is 0.25 m long when loosening a bolt.
Calculate the moment of the force about the bolt, and state its direction if the spanner turns clockwise.
Mark scheme:
Correct use of equation moment = force × perpendicular distance (1 mark)
Correct calculation: 12 × 0.25 = 3.0 N m (1 mark)
Award full marks only if correct unit (N m) and direction (clockwise) are stated
Question 2 (5 marks)
A uniform beam of length 2.0 m and weight 40 N is supported horizontally by a pivot 0.5 m from one end. A load of 60 N is suspended from the shorter end of the beam.
(a) Draw a labelled diagram showing all forces acting on the beam.
(b) Calculate the reaction force at the pivot, assuming the beam is in equilibrium.
(c) State the principle of moments and explain how it applies in this situation.
Mark scheme:
(a) Diagram showing:
Weight of beam (40 N) acting at its centre (1.0 m from either end) (1 mark)
Load (60 N) acting downward at shorter end (0.5 m from pivot) (1 mark)
Upward reaction at pivot (1 mark)
(b) Use of principle of moments: sum of clockwise moments = sum of anticlockwise moments (1 mark)
Correct calculation using moments about the pivot:
Clockwise moment = 60 × 0.5 = 30 N m
Anticlockwise moment = 40 × (1.0 − 0.5) = 20 N m
Net upward reaction = total downward force − (difference in moments / lever arm if calculated correctly) (1 mark)Correct final reaction force = 100 N (1 mark)
(c) States the principle of moments: for a body in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about any point (1 mark)
Explains that the pivot provides a reaction force balancing both the vertical forces and turning effects (1 mark)
