← All notesPhysics · Forces, moments & momentum⬇ Download PDF
IGCSE Physics 0625 · Chapter 3 notes · ~10 min read

Forces, moments & momentum

Everything that pushes, pulls, turns and crashes — from springs and friction to see-saws and car safety.

Resultant forceSprings & Hooke's lawFriction & dragF = maCircular motionMomentsCentre of gravityMomentum & impulse
RSby Riyaz Sir
mentorriyaz.in
No tag = Core (everyone)EXTENDED Extended onlyhighlight = comes up again and againTest yourself at the end

In 30 seconds

  • A resultant force changes motion. Zero resultant = stays at rest or keeps moving at constant velocity.
  • Moment = force × perpendicular distance. Balanced when clockwise moments = anticlockwise moments.
  • EXT F = ma, F = kx (springs) and momentum p = mv (conserved in collisions).
  • A low centre of gravity and a wide base make an object stable.

By the end you can

  • Combine forces on a line and say what a resultant force does.
  • Plot and interpret a load–extension graph and use F = kx. EXT
  • Use F = ma and describe circular motion qualitatively. EXT
  • Calculate moments and apply the principle of moments.
  • Find the centre of gravity of a lamina and judge stability.
  • Calculate momentum and impulse and use conservation of momentum. EXT

1Forces and motion

The effect of forces

  • A force is a push or a pull, measured in newtons (N). It can change an object's size, shape, speed or direction.
  • The resultant force is the single force that has the same effect as all the forces together. On a line: add forces in the same direction, subtract forces in opposite directions.
  • Resultant = 0 (balanced forces): an object at rest stays at rest, and a moving object keeps the same speed in a straight line.
  • Resultant ≠ 0: the object speeds up, slows down, or changes direction.
Picture itIn a tug-of-war, if both teams pull with 800 N the rope does not move. If one team pulls with 900 N against 800 N, there is a resultant of 100 N towards the stronger team and the rope accelerates that way.
Common mistake"A moving object always needs a force to keep it moving." No — at constant speed the forces are balanced (resultant zero).

Friction and drag

  • Friction is a force between surfaces in contact. It opposes motion and makes the surfaces heat up.
  • Drag is friction in a liquid or gas (air resistance). It grows as the speed grows.
  • Useful: brakes, grip of shoes and tyres. A nuisance: wasted energy as heat in machines (fixed by oil or lubricant).

Newton's second lawEXTENDED

F = m a
resultant force (N) = mass (kg) × acceleration (m/s²)
  • The acceleration is in the same direction as the resultant force. 1 N is the force that gives a 1 kg mass an acceleration of 1 m/s².
  • Same force on a bigger mass → smaller acceleration.
Worked example

A 1200 kg car has a driving force of 3500 N and a resistive force of 500 N. Find its acceleration.

  1. Resultant force = 3500 − 500 = 3000 N
  2. a = F ÷ m = 3000 ÷ 1200
  3. = 2.5 m/s² in the direction of the driving force
Common mistakeUsing the driving force alone in F = ma. Use the RESULTANT force.

Circular motionEXTENDED

velocity(tangent)force towardsthe centredirection keeps changing → a resultant force is needed
The velocity is always along the tangent. A force towards the centre keeps changing the direction.
  • Moving in a circle at constant speed means the direction keeps changing, so the velocity changes and the object is accelerating. A resultant force acts towards the centre.
  • The force needed is bigger for a larger mass, a higher speed and a smaller radius.
  • Examples: the Moon around the Earth (gravity), a car on a bend (friction), a stone on a string (tension).

2Springs and Hooke's law

Load–extension graphs

  • Extension x = new length − original length.
  • Hang masses (the load) on a spring and measure the length each time. Subtract the original length to get extension, then plot load (force) against extension.
extensionforceF = kxk = gradientlimit of proportionalitystraight line through the origin = Hooke’s law
A straight line through the origin means force is proportional to extension — Hooke's law. The line bends beyond the limit of proportionality.
  • Up to the limit of proportionality the extension is directly proportional to the load. Beyond it the spring stretches more for each extra newton and may not return to its original length.
EXT F = k x
k = spring constant (N/m) = gradient of the straight part; x = extension (m)
Worked example

EXT A spring has k = 40 N/m. What force gives an extension of 6.0 cm?

  1. Convert: 6.0 cm = 0.060 m
  2. F = kx = 40 × 0.060
  3. = 2.4 N
Common mistakeUsing the total length instead of the extension.
Exam tipDescribing the experiment: measure the original length, add equal masses one at a time, measure the length each time, subtract to get extension, plot the graph. Use a ruler fixed vertically beside the spring and read at eye level.

3Turning effects

Moments

Moment — the turning effect of a force about a pivot.

moment = F × d
unit N m · d = the PERPENDICULAR distance from the pivot to the line of action of the force
  • Examples: pushing a door at the handle (large d) is much easier than near the hinge (small d); a spanner; a see-saw.
F₁F₂d₁d₂pivotbalanced when F₁ × d₁ = F₂ × d₂
A balanced beam: the clockwise moment (F₂ × d₂) equals the anticlockwise moment (F₁ × d₁).

Principle of moments and equilibrium

sum of clockwise moments = sum of anticlockwise moments
when the object is balanced
  • An object is in equilibrium if the resultant force is zero AND the resultant moment is zero.
  • EXT With several forces on each side, add up all the clockwise moments and all the anticlockwise moments.
Worked example

A see-saw pivots in the middle. A 300 N child sits 2.0 m from the pivot. Where must a 400 N child sit to balance?

  1. Anticlockwise = clockwise
  2. 300 × 2.0 = 400 × d
  3. 600 = 400d
  4. d = 1.5 m from the pivot
Common mistakeMeasuring the distance along a slanted line. d must be perpendicular to the force.

Centre of gravity and stability

Centre of gravity (CG) — the point where the whole weight of an object seems to act.

pinplumb linehang it, mark the plumb lineAB1: from hole A (red)2: from hole B (blue)crossing = centre of gravity
Hang the lamina from a pin, mark the plumb line, repeat from another hole. The lines cross at the centre of gravity.
  • Stable objects: low CG and a wide base. The object topples when the vertical line from the CG falls outside the base.
line from CG falls outsidethe base → topples ✗line falls inside thebase → stable ✓a CG that stays above the base = stable
A tipped object returns if the line from its CG falls inside the base; it topples if the line falls outside.
  • Examples: a double-decker bus is tested by tilting it; racing cars are low and wide; a bus with passengers downstairs is safer.

4Momentum

Momentum and impulseEXTENDED

p = m v
momentum (kg m/s) = mass (kg) × velocity (m/s) — a vector, same direction as the velocity
impulse = F Δt = Δ(mv)
force × time the force acts = change in momentum
F = ΔpΔt
resultant force = rate of change of momentum
  • Conservation of momentum: in a collision with no outside forces, total momentum before = total momentum after. Choose one direction as positive.
beforeA 2 kg3 m/sB 1 kgat restafter (they stick together)AB2 m/smomentum before = 2 × 3 = 6 | after = 3 × 2 = 6 ✓
Momentum is shared out but the total is the same: 6 kg m/s before and after.
Worked example

A 2.0 kg trolley moving at 3.0 m/s hits a stationary 1.0 kg trolley. They stick together. Find the speed afterwards.

  1. Momentum before = 2.0 × 3.0 + 1.0 × 0 = 6.0 kg m/s
  2. Momentum after = (2.0 + 1.0) × v = 3.0v
  3. 6.0 = 3.0v
  4. v = 2.0 m/s in the original direction
Picture itCatching a fast cricket ball: if you pull your hands back, the ball's momentum changes to zero over a longer time, so the force on your hands is smaller.
  • Safety: crumple zones, air bags, seat belts, padded helmets and playground surfaces all increase the time of the collision, so the force is smaller for the same change of momentum.

5Test yourself

Test yourself — cover the answers first

Quick check

  1. Resultant of 12 N to the right and 5 N to the left?
  2. Moment of a 20 N force acting 0.30 m from a pivot?
  3. A 1200 kg car has a resultant force of 3000 N. What is its acceleration?
  4. State the unit of momentum.
  5. What must be true for an object to be in equilibrium?
  6. Why is a car with a low centre of gravity more stable?

Exam-style

  1. A spring is 12.0 cm long. A load of 5.0 N makes it 17.0 cm long. Assuming it obeys Hooke's law, find the spring constant.
  2. A uniform 40 N plank rests on a pivot at its centre. A 60 N weight hangs 0.50 m to the left. How far to the right of the pivot must a 20 N weight hang to balance?
  3. A 0.60 kg trolley moving at 2.0 m/s collides with a 0.40 kg trolley at rest. They join together. Calculate the speed after the collision.
  4. Explain why an air bag reduces injury in a crash. [2]
Show answers
  1. 7 N to the right
  2. 20 × 0.30 = 6.0 N m
  3. 3000 ÷ 1200 = 2.5 m/s² EXT
  4. kg m/s EXT
  5. resultant force = 0 and resultant moment = 0
  6. The line from its CG stays inside the base until the car is tilted much further.
  7. extension = 17.0 − 12.0 = 5.0 cm = 0.050 m
    k = F ÷ x = 5.0 ÷ 0.050 = 100 N/m
  8. The plank's own weight acts at the pivot, so it adds no moment
    60 × 0.50 = 20 × d
    d = 30 ÷ 20 = 1.5 m
  9. momentum before = 0.60 × 2.0 = 1.2 kg m/s
    total mass = 1.0 kg
    v = 1.2 ÷ 1.0 = 1.2 m/s
  10. It increases the time taken for the passenger to stop
    so the rate of change of momentum, and hence the force, is smaller
Practise this chapter
Effects of forcesTurning effect & centre of gravityMomentum
Next chapterEnergy, work & power →
Stuck on a question?

Send it to me on WhatsApp. I read every message.

Want regular help? Send this to your parent →
Share with a friendAsk Riyaz Sir