In simple terms
A friendly intro before the formal notes — no formulas yet.
Turning effects of forces
Cambridge 9702 Paper 2 — Turning effects of forces (4.1). This lesson covers the concepts of moments, centre of gravity, couples, torque, and the conditions for equilibrium, supported by worked examples and key definitions.
- 1
4.1 Turning effects of forces.
- 2
The centre of gravity of an object is the point at which the weight of the object may be considered to act.
- 3
For uniform objects, the CoG is at the geometric centre.
- 4
In a uniform gravitational field, CoG and CoM are at the same point.
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 4.1.1
Understand that the weight of an object may be taken as acting at a single point known as its centre of gravity
- 4.1.2
Define and apply the moment of a force
- 4.1.3
Understand that a couple is a pair of forces that acts to produce rotation only
- 4.1.4
Define and apply the torque of a couple
Explore the concept
Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.
Step-synced diagram — highlights what to look for in the simulation above.
Step 1
4.1 Turning effects of forces.
15 more simulations for this topic — run them in the Simulations section below
Simulations
Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.
15 simulations · 5 to start with
Start herein this order — each one shows a different piece of the topic
- The Physics ClassroomStart here · 19702 4.1 · IB A.4
Torque Balancer
One to four torques are placed on the right of the fulcrum; add torques on the left to balance the beam and check your answer
Why this one: Add up the moments on the right, then place masses on the left until the sums match.
Try this
- Add up the torques on the right of the fulcrum.
- Add torques on the left to match.
- Check and try the next beam.
Look for The beam balances when the sum of anticlockwise moments equals the sum of clockwise moments.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- 3JCN PhysicsStart here · 29702 4.1 · 9702 4.2 · IB A.4
Torque - Measure Beam Mass
Balance a beam with known masses to deduce the beam's own mass from moments
Why this one: The beam's own weight acts at its centre of gravity; take moments to find that hidden mass.
Try this
- Balance the beam using a known mass at a chosen position.
- Take moments about the pivot to deduce the beam's own mass.
- Repeat with a different known mass and compare your result.
Look for The beam's weight acts at its centre of mass, and balance equates its moment with the known mass's moment.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- The Physics ClassroomStart here · 39702 4.1 · IB A.4
Center of Mass
Drag out a shape, view its centre of mass as you change it, then hang it on the corkboard and watch it swing about the pivot
Why this one: Hang any shape and it settles with its centre of mass directly below the pivot.
Try this
- Drag out a shape and watch the centre of mass.
- Add material to one side and watch it move.
- Hang the shape and watch where it settles.
Look for A hung shape comes to rest with its centre of mass directly below the pivot.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- oPhysicsStart here · 49702 4.1 · 9702 4.2 · IB A.2
Stability, Equilibrium, and Center of Mass
Tilt objects to explore stability, equilibrium and where the centre of mass must sit over the base
Why this one: Tilt an object until its centre of mass passes outside the base: that is the moment it topples.
Try this
- Tilt an object until it topples.
- Try an object with a wider base.
- Lower the centre of mass and tilt again.
Look for An object topples once its centre of mass passes outside its base; a wider base or lower centre of mass needs a larger tilt.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- SimuPhysicsStart here · 59702 4.1 · IB A.4
Torque due to a Couple
Two equal and opposite forces produce pure rotation with no net force; move the measuring point and the turning effect is unchanged
Why this one: Two equal, opposite forces give zero net force but a moment F × d, the same about any point.
Try this
- Apply the couple and read the net force.
- Move the point you measure the moment about.
- Change the separation of the two forces.
Look for The moment of a couple equals one force multiplied by the perpendicular distance between them, about any point.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
More simulations10 more on this topic — core ones first
- oPhysicsCore9702 4.1 · 9702 4.2 · IB A.4
Equilibrium Problem: Bar with Axis Supported by a Cable
Uniform bar hinged at one end, held by a cable, with a movable mass; find cable tension and hinge force
Try this
- Slide the mass along the bar and read the cable tension.
- Move the mass to the far end.
- Compare the hinge force at both positions.
Look for Taking moments about the hinge, the cable tension rises as the mass moves outward.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- The Physics ClassroomCore9702 4.1 · IB A.4 · IB A.2
Balance Beam
Hang weights at different positions on a balance beam and work out what it takes to balance
Try this
- Hang equal weights at equal distances from the pivot.
- Move one weight further out.
- Balance a heavy weight with a lighter one.
Look for The beam balances when weight times distance is equal on each side.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- The Physics ClassroomCore9702 4.2 · 9702 4.1 · IB A.4
Static Equilibrium
A rod leans against a wall; control the lengths, masses and angles and see how each affects the forces
Try this
- Change the angle and read the force from the wall.
- Change the mass and compare the forces.
- Change the length and compare.
Look for In equilibrium the forces and the moments about any point both sum to zero.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- SimuPhysicsCore9702 4.1 · IB A.4
Torque on a Wheel
Apply a force to a wheel at any point and any angle and see how the perpendicular distance to the axle governs the turning effect
Try this
- Apply a force at the rim and read the torque.
- Move the force closer to the axle.
- Change the angle of the force.
Look for Torque equals force multiplied by the perpendicular distance from the axle to its line of action.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- 3JCN PhysicsCore9702 4.1 · 9702 4.2 · IB A.4
Torque - Balancing Act
Hang masses on a beam at chosen positions to balance it about a pivot
Try this
- Hang one mass on each side at equal distances from the pivot and check balance.
- Double one mass and move it to half the distance; check balance again.
- Hang two masses on one side and balance them with one mass on the other.
Look for The beam balances when the clockwise and anticlockwise moments about the pivot are equal.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsCore9702 4.2 · 9702 4.1 · IB A.2
Static Equilibrium Problem 1
Static equilibrium problem 1: adjust forces and solve for unknown tensions
Try this
- Adjust the forces and solve for the unknown tensions.
- Check that the horizontal and vertical components each sum to zero.
Look for In equilibrium the resultant force is zero, so components balance in each direction.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
Key formulas
Tap any symbol to reveal exactly what it means and its units.
Tap a symbol — great for exam definitions
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Full topic notes
Formal explanation with the rigour you need for the exam.
Centre of Gravity (CoG) and Centre of Mass (CoM)
Every object has a special point where its entire weight seems to act – this is its Centre of Gravity (CoG). Imagine balancing an object; the CoG is the point you'd try to support. For uniform objects (like a perfectly symmetrical ruler), the CoG is usually at its geometric centre.
Closely related is the Centre of Mass (CoM), which is the average position of all the mass in an object. While distinct in theory, in typical Cambridge Physics scenarios (where the gravitational field is considered uniform), the CoG and CoM are located at the exact same point. So, for most calculations, you can treat them as identical.
For an irregular shape, like a piece of cardboard, the CoG can be found experimentally. By suspending the object from a point and hanging a plumb line from the same point, you can trace the vertical line where the CoG must lie. Repeating this from a different suspension point gives a second line. The CoG is where these two lines intersect.
4.1 Turning effects of forces.
The centre of gravity of an object is the point at which the weight of the object may be considered to act.
For uniform objects, the CoG is at the geometric centre.
In a uniform gravitational field, CoG and CoM are at the same point.
Moment of a Force
The moment of a force quantifies its ability to cause rotation about a specific point, called the pivot. Think of it as the turning power. A larger force or a greater distance from the pivot will create a larger moment, making it easier to rotate the object.
M represents the moment of the force.
F is the magnitude of the force.
is the perpendicular distance from the pivot to the line of action of the force.
The unit for moment is Newton-metre (Nm).
Moments are vector quantities; they have a direction (clockwise or anticlockwise).
Always remember that 'd' must be the perpendicular distance from the pivot to the line of action of the force. If the force isn't perpendicular, you'll need to use trigonometry to find the correct perpendicular component of the distance or the perpendicular component of the force.
Principle of Moments
For an object to be in rotational equilibrium – meaning it's either stationary or rotating at a constant angular velocity (not accelerating angularly) – the turning effects in one direction must perfectly balance the turning effects in the opposite direction. This is the Principle of Moments.
For rotational equilibrium, the resultant moment is zero.
Sum of clockwise moments = Sum of anticlockwise moments.
This principle is vital for analysing balanced systems like levers, seesaws, and bridges.
Couples and Torque
Sometimes, two specific forces combine to produce a pure turning effect without any linear movement. This arrangement is called a couple. A couple consists of two forces that are equal in magnitude, opposite in direction, parallel to each other, but act along different lines. Examples include turning a steering wheel with both hands or using a key to open a lock.
The turning effect produced by a couple is called torque (often represented by ). Unlike the moment of a single force, the torque of a couple is the same regardless of where you choose your pivot point. It causes rotation only.
F is the magnitude of one of the forces in the couple.
d is the perpendicular distance between the lines of action of the two forces.
The unit for torque is also Newton-metre (Nm).
A couple produces pure rotation, with no resultant linear force.
Equilibrium
For an object to be in complete equilibrium, it must satisfy two conditions simultaneously: it must not be accelerating linearly, and it must not be accelerating rotationally. This means no overall push/pull and no overall turning effect.
Condition 1: Zero resultant force. The vector sum of all forces is zero. This means the sum of forces in any direction is zero (e.g., sum of upward forces = sum of downward forces, and sum of leftward forces = sum of rightward forces).
Condition 2: Zero resultant moment. The sum of clockwise moments about any point equals the sum of anticlockwise moments about that same point.
Both conditions must be met for an object to be truly 'in equilibrium'.
Stability of an Object
The stability of an object is its ability to return to its original position after being slightly displaced. It is determined by the position of its Centre of Gravity (CoG). An object is most stable when its CoG is as low as possible and its base area is as wide as possible. There are three types of equilibrium:
Stable Equilibrium: If displaced, the object's CoG is raised. When released, its weight creates a restoring moment that returns it to its original position (e.g., a cone resting on its base).
Unstable Equilibrium: If displaced, the object's CoG is lowered. Its weight creates a moment that causes it to topple over and find a more stable position (e.g., a cone balanced on its tip).
Neutral Equilibrium: If displaced, the object's CoG remains at the same height. It stays in the new position without tending to move back or topple further (e.g., a ball on a horizontal surface).
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A uniform beam, 3.0 m long and weighing 50 N, is pivoted at its centre. A 20 N weight is placed 1.0 m from the left end. Where should a 30 N weight be placed to balance the beam?
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Identify pivot and forces: The pivot is at the centre of the beam (1.5 m from either end). The beam's own weight acts at the pivot, so it creates no moment.
A uniform 4.0 m long rod with a weight of 120 N is hinged to a vertical wall. It is held horizontally by a cable attached to the end of the rod and to a point on the wall. The cable makes an angle of 30° with the rod. Calculate the tension (T) in the cable.
- 1
Identify the pivot and forces: The pivot is the hinge. The forces creating moments are the weight of the rod (acting downwards at its centre) and the tension in the cable (acting upwards at an angle).
How it all connects
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Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.
Glossary
Key terms for this topic — skim now; the Check step will test them.
- Centre of Mass (CoM)
Closely related is the Centre of Mass (CoM), which is the average position of all the mass in an object.
- rotational equilibrium
Meaning it's either stationary or rotating at a constant angular velocity (not accelerating angularly) – the turning effects in one direction must perfectly balance the turning effects in the opposite direction.
- torque
The turning effect produced by a couple is called torque (often represented by ).
- complete equilibrium
For an object to be in complete equilibrium, it must satisfy two conditions simultaneously: it must not be accelerating linearly, and it must not be accelerating rotationally. This means no overall push/pull and no overall turning effect.
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
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Teach it back
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Revision flashcards
Guess first, then flip — retrieval beats re-reading.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
4.1 Turning effects of forces.
The centre of gravity of an object is the point at which the weight of the object may be considered to act.
For uniform objects, the CoG is at the geometric centre.
In a uniform gravitational field, CoG and CoM are at the same point.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Use the principle of moments to show that the upthrust U exerted by the water on the cylinder is 1.4 N.
By taking moments about A, determine the tension in the wire.
Extra simulations & links
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Frequently asked
Checkpoint
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