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Motion, forces and energy

IGCSE Physics 0625 · Unit 1 revision notes

Measurement, motion graphs, mass and weight, density, forces and moments, momentum, energy, work, power and pressure: every definition, equation, graph and trap on one page.

49 definitions to learn word for word, 34 equations in their own column, 35 diagrams and graphs. Read it, cover it, test yourself.

  1. 1.1a Measuring length, volume and time
  2. 1.1b Scalars and vectors
  3. 1.2a Speed, velocity and distance-time graphs
  4. 1.2b Speed-time graphs and acceleration
  5. 1.2c Free fall and terminal velocity
  6. 1.3 Mass and weight
  7. 1.4 Density
  8. 1.5a Resultant force, friction and motion
  9. 1.5b Springs and Hooke's law
  10. 1.5c Turning effect of forces (moments)
  11. 1.5d Centre of gravity and stability
  12. 1.6 Momentum
  13. 1.7a Energy stores, transfers and conservation
  14. 1.7b Work
  15. 1.7c Energy resources and efficiency
  16. 1.7d Power
  17. 1.8a Pressure on surfaces
  18. 1.8b Pressure in liquids
Definitions (mark-scheme wording)EquationsExam trapsExtended = Extended tier only

1.1aMeasuring length, volume and time

Definitions

Meniscus
the curved surface of a liquid in a tube; for water, read the volume at the bottom of the meniscus.
Oscillation (one)
one complete swing, from one side to the other and back again.

Key points

  • Length: metre rule or tape, read to the nearest mm; look straight at the scale to avoid parallax.
  • Volume of a liquid: measuring cylinder on a flat surface, eye level with the bottom of the meniscus.
  • Time: stopwatch, clock or digital timer (light gates for very short times).
  • Short interval: time many repeats and divide, e.g. time 20 swings, then period = total time / 20.
  • Small length: measure a stack and divide, e.g. thickness of 100 sheets / 100.
  • Timing many repeats makes the stopwatch reaction-time error a smaller fraction of the total.
50 cm³ eye level read the bottom of the meniscus
Read a measuring cylinder with your eye level with the bottom of the meniscus.
there and back = 1 oscillation T = t / 20 fiducialmark atcentre
Pendulum: one oscillation is there and back. Time 20 of them and divide by 20.

Watch out!

  • Reading the top of a water meniscus, or reading from above or below eye level (parallax).
  • Forgetting to divide by the number of swings or sheets at the end.

1.1bScalars and vectors

Definitions

Scalar
Extended a quantity that has magnitude (size) only.
Vector
Extended a quantity that has magnitude and direction.
Resultant
the single vector that has the same effect as two or more vectors acting together.

Key points

  • Extended scalars: distance, speed, time, mass, energy, temperature.
  • Extended vectors: displacement, velocity, acceleration, force, weight, momentum, electric field strength, gravitational field strength.
  • Vectors along the same line: add if in the same direction, subtract if opposite.
  • Extended two vectors at right angles: resultant by Pythagoras, direction by tan θ.
  • Extended or by scale drawing: draw head to tail to scale, measure the resultant and its angle.
E distance = 8 m (scalar) AB displacement = 5 m east (vector)
Distance follows the path walked; displacement is the straight line from A to B, with a direction.
θ 3 N 4 N R R² = 3² + 4² R = 5 N tan θ = 4 / 3 θ = 53°
Extended: 3 N east and 4 N north, drawn head to tail, give a 5 N resultant at 53° north of east.

Watch out!

  • Extended: never add the sizes of perpendicular vectors: 3 N and 4 N at right angles give 5 N, not 7 N.
  • A vector answer needs a direction as well as a size.

1.2aSpeed, velocity and distance-time graphs

Definitions

Speed
the distance travelled per unit time.
Velocity
the speed in a given direction.
Average speed
the total distance travelled divided by the total time taken.

Key points

  • Distance-time graph: gradient = speed.
  • Horizontal line: at rest. Straight sloping line: constant speed.
  • Curving upwards (getting steeper): accelerating. Flattening: decelerating.
  • Steeper line = faster.
  • Speed from a straight section: draw a large triangle, gradient = Δd / Δt.
  • Velocity can change even at constant speed, if the direction changes.
d / mt / s constant speed at rest accelerating
Distance-time shapes: steeper = faster, flat = at rest, curving up = accelerating.
d / mt / s Δt = 6 s Δd = 120 m gradient = speed
Speed = gradient of a straight section = Δd / Δt = 120 / 6 = 20 m/s.

Watch out!

  • Average speed uses the total time, including time spent stationary.
  • Convert units first: km to m (× 1000), minutes to s (× 60).

1.2bSpeed-time graphs and acceleration

Definitions

Acceleration
Extended the change in velocity per unit time.
Deceleration
Extended a negative acceleration (the velocity decreases).

Key points

  • Speed-time graph: horizontal line = constant speed; sloping up = accelerating; sloping down = decelerating.
  • Line along the time axis (speed = 0) = at rest.
  • Area under the line = distance travelled. Split it into rectangles and triangles.
  • Extended gradient = acceleration; a negative gradient is a deceleration.
  • Extended a straight line = constant acceleration; a curve = changing acceleration.
  • Extended curve getting less steep = acceleration decreasing (e.g. a falling object meeting air resistance).
v / m/st / s 20 81622 speeding up constant speed braking 8016060
Accelerate, cruise, brake. Total distance = shaded area = 80 + 160 + 60 = 300 m.
v / m/st / s steep: large a shallow: small a
Extended: a curve that flattens means the acceleration (gradient of the tangent) is decreasing.

Watch out!

  • Gradient = acceleration, but area = distance. Do not swap them.
  • A flat line on a speed-time graph means constant speed, not stopped. Check the axis label.

1.2cFree fall and terminal velocity

Definitions

Acceleration of free fall (g)
the acceleration of an object falling with no air resistance; near the Earth it is constant, about 9.8 m/s2.
Terminal velocity
Extended the constant velocity reached when the air resistance on a falling object equals its weight.

Key points

  • Near the Earth, g ≈ 9.8 m/s2, the same for all masses when air resistance is negligible.
  • Extended no air resistance: speed-time graph is a straight line with gradient g.
  • Extended at the start, speed is low, so drag is small and acceleration ≈ g.
  • Extended as speed increases, drag increases, the resultant force falls, so acceleration decreases.
  • Extended when drag = weight, resultant force = 0, acceleration = 0: terminal velocity.
  • Extended opening a parachute increases drag, so the object decelerates to a new, lower terminal velocity.
v / m/st / s no air resistance(gradient = g) terminal velocity
Extended: without air resistance v rises steadily; with air resistance the curve levels off at terminal velocity.
WWW dragdrag starta = g fastera < g drag = Wa = 0
Extended: forces on a falling object. Drag grows with speed until it balances the weight.

Watch out!

  • Extended: at terminal velocity the object is still moving; it is the acceleration that is zero, not the speed.
  • Extended: opening a parachute does not make the skydiver move upwards; it slows the fall.

1.3Mass and weight

Definitions

Mass
a measure of the quantity of matter in an object at rest relative to the observer.
Weight
a gravitational force on an object that has mass.
Gravitational field strength (g)
the force per unit mass.
Weight (field view)
Extended the effect of a gravitational field on a mass.

Key points

  • Mass is in kg and is the same everywhere; weight is a force in N and depends on g.
  • Near the Earth's surface g = 9.8 N/kg; on the Moon g is about 1.6 N/kg.
  • Weights (and so masses) are compared using a balance; a force meter (newtonmeter) measures weight.
  • g in N/kg is numerically equal to the acceleration of free fall in m/s2.
  • Extended weight acts towards the centre of the Earth (or other body).
1 kg W reads9.8 N Earth: g = 9.8 N/kg W = 9.8 N Moon: g = 1.6 N/kg W = 1.6 N mass = 1 kg in both
A force meter reads weight. The same 1 kg mass weighs less on the Moon, but its mass does not change.
W / Nm / kg gradient = g ΔmΔW
Weight is proportional to mass: W against m is a straight line through the origin with gradient g.

Watch out!

  • Weight is a force: give it in newtons, never kg. A 60 kg student weighs 60 × 9.8 = 588 N.
  • Going to the Moon changes weight, not mass.

1.4Density

Definitions

Density
the mass per unit volume.

Key points

  • Water: 1.0 g/cm3 = 1000 kg/m3.
  • Regular solid: measure the sides with a rule, calculate V (e.g. l × w × h), find m with a balance.
  • Liquid: mass of empty cylinder, then with liquid; subtract. Read V from the cylinder.
  • Irregular solid: volume by displacement: rise in water level in a measuring cylinder, or the overflow from a displacement (eureka) can.
  • An object floats if its density is less than the liquid's, sinks if greater.
  • Extended a liquid floats on another liquid that is denser (if they do not mix), e.g. oil on water.
V = V2 - V1 = 20 cm³ add object V1 = 50 cm³ V2 = 70 cm³
Displacement: the rise in water level equals the volume of the object.
floats: ρ < ρ of liquid sinks: ρ > ρ of liquid liquid
Float or sink: compare the object's density with the liquid's density.

Watch out!

  • g/cm3 to kg/m3: multiply by 1000, not 100. 0.8 g/cm3 = 800 kg/m3.
  • Displacement gives the volume of the object, not its mass.

1.5aResultant force, friction and motion

Definitions

Resultant force
the single force that has the same effect as all the forces acting on an object.
Newton's first law
an object stays at rest or moves at constant velocity (constant speed in a straight line) unless acted on by a resultant force.
Solid friction
the force between two surfaces that may impede motion and produce heating.
Drag
friction acting on an object moving through a liquid or a gas; air resistance is a form of drag.
Newton's second law
Extended the resultant force equals mass × acceleration, and the acceleration is in the direction of the resultant force.

Key points

  • A force can change an object's size and shape, its speed or its direction.
  • Forces along a line: add those in the same direction, subtract opposite ones.
  • Zero resultant: at rest, or constant speed in a straight line (forces balanced).
  • Non-zero resultant: the velocity changes (speeds up, slows down or changes direction).
  • Friction and drag oppose motion; drag increases with speed.
  • Extended a force perpendicular to the velocity makes an object move in a circle at constant speed.
  • Extended for circular motion a larger force is needed if the speed increases, the radius decreases or the mass increases.
10 N 4 N resultant = 6 N to the right thrust 500 N drag 500 N balanced: at rest or constant velocity
Top: 10 N and 4 N in opposite directions give a 6 N resultant. Bottom: balanced forces, so no change in velocity.
v F Bigger F if: speed increases radius decreases mass increases
Extended: circular motion. The velocity is along the tangent; the force is towards the centre, at 90° to the velocity.

Watch out!

  • Balanced forces do not mean the object is at rest: it may be moving at constant velocity.
  • Extended: in F = ma, F is the resultant force, not just the driving force.

1.5bSprings and Hooke's law

Definitions

Extension
the increase in length of a spring from its original (unstretched) length.
Load
the force (usually a weight) that stretches the spring.
Hooke's law
Beyond the syllabus (name not required): the extension of a spring is directly proportional to the load, up to the limit of proportionality.
Spring constant (k)
Extended the force per unit extension.
Limit of proportionality
Extended the point beyond which the extension is no longer directly proportional to the load.

Key points

  • Experiment: hang the spring from a clamp, measure its original length against a vertical metre rule.
  • Add masses one at a time; record the length each time; extension = length - original length.
  • Load from masses: W = mg (100 g gives about 1 N).
  • Read the rule at eye level, using a pointer fixed to the bottom of the spring.
  • Load-extension graph: a straight line through the origin while the extension is proportional to the load.
  • Extended past the limit of proportionality the line curves (no longer straight); identify this point on the graph.
metre rule spring pointer slottedmasses clamp stand
Stretching a spring: add slotted masses and read the pointer against the metre rule each time.
F / Nx / cm limit ofproportionality gradient = k F ∝ x here
Load-extension: straight through the origin up to the limit of proportionality (gradient = k when F is plotted up the side).

Watch out!

  • x is the extension, not the total length of the spring.
  • Extended: masses in g must become a force in N (W = mg) before using k = F / x.

1.5cTurning effect of forces (moments)

Definitions

Moment of a force
the product of the force and the perpendicular distance from the pivot to the line of action of the force.
Principle of moments
for an object in equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about the same point.
Equilibrium
the state of an object when there is no resultant force and no resultant moment on it.

Key points

  • A moment is the turning effect of a force; unit N m.
  • Bigger moment from a bigger force or a longer distance: long spanners, door handles far from the hinge.
  • Use the perpendicular distance from the pivot to the line of action.
  • Balancing a see-saw: a heavier person sits closer to the pivot.
  • Extended with several forces on each side, add all clockwise moments and all anticlockwise moments.
  • Extended to verify, balance a metre rule on a pivot, hang masses, adjust until level, then compare the two sums.
30 N 20 N 2 m 3 m 30 × 2 = 20 × 3 = 60 N m anticlockwise clockwise
Balanced beam: anticlockwise moment 30 × 2 = clockwise moment 20 × 3 = 60 N m.
4 N 2 N 2 N 30 cm 20 cm 40 cm 4 × 30 = 2 × 20 + 2 × 40 120 N cm = 120 N cm
Extended: two forces on one side. Anticlockwise 4 × 30 = 120 N cm; clockwise 2 × 20 + 2 × 40 = 120 N cm.

Watch out!

  • Use the perpendicular distance to the pivot, not the distance along a slanted line.
  • Take all moments about the same pivot, and keep units consistent (N m or N cm).

1.5dCentre of gravity and stability

Definitions

Centre of gravity
the point through which all the weight of an object appears to act.

Key points

  • Plane lamina: hang it from a pin through a hole so it swings freely; hang a plumb line from the same pin.
  • Mark the plumb line on the lamina; repeat from a second hole. The centre of gravity is where the lines cross.
  • An object is stable if, when tilted, the vertical line through its centre of gravity stays inside its base.
  • If that line falls outside the base, the weight gives a moment that topples it.
  • More stable: low centre of gravity and wide base (racing cars, bus design, Bunsen burner bases).
  • A regular shape of uniform density has its centre of gravity at its geometric centre.
12 CG plumb line pin throughhole 1, thenhole 2
Plumb-line method: the lines from two holes cross at the centre of gravity (CG).
CG line inside: falls back line outside: topples
Tilted objects: the low, wide block falls back; the tall, narrow one topples because its CG line is outside the base.

Watch out!

  • The centre of gravity can lie outside the material, e.g. for a ring or an L-shape.
  • Stability depends on where the CG line falls relative to the pivot edge of the base, not on the mass alone.

1.6Momentum Extended

Definitions

Momentum
Extended mass × velocity.
Impulse
Extended force × time for which the force acts; it equals the change in momentum.
Principle of conservation of momentum
Extended when no resultant external force acts on a system, the total momentum before an interaction equals the total momentum after it.
Resultant force (momentum form)
Extended the change in momentum per unit time.

Key points

  • Extended momentum is a vector, in the direction of the velocity.
  • Extended choose a positive direction; anything moving the other way has negative momentum.
  • Extended conservation applies to collisions and explosions.
  • Extended objects that stick together move off with the combined mass.
  • Extended explosion from rest: total momentum stays zero, so the parts have equal and opposite momenta.
  • Extended crumple zones, airbags and seat belts increase the time of impact, so the force is smaller for the same Δp.
  • Extended units: kg m/s = N s.
before 2 kg 3 m/s 1 kg at rest after 2 kg 1 kg 2 m/s before: 2 × 3 = 6 kg m/s after: 3 × 2 = 6 kg m/s
Extended: a sticking collision. The trolleys share the momentum; the total, 6 kg m/s, is unchanged.
before 1 kg 2 kg at rest: p = 0 after 1 kg 4 m/s 2 kg 2 m/s equal and opposite momenta
Extended: an explosion from rest. Total momentum is zero before and after: 2 × 2 + 1 × (-4) = 0.

Watch out!

  • Forgetting the minus sign for motion in the opposite direction before adding momenta.
  • Kinetic energy is not always conserved in a collision, but momentum always is (no external force).

1.7aEnergy stores, transfers and conservation

Definitions

Principle of conservation of energy
energy cannot be created or destroyed; it can only be transferred from one store to another.
Kinetic energy
the energy an object has because of its motion.
Gravitational potential energy
the energy an object has because of its position (height) in a gravitational field.

Key points

  • Stores: kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic, internal (thermal).
  • Transfers: mechanical work (forces), electrical work (currents), heating, and waves (electromagnetic, sound).
  • Wasted energy is usually dissipated to the surroundings as internal energy, by heating.
  • Energy flow diagram: shows the stores and transfers; total energy in = total energy out.
  • Extended Sankey diagram: arrow widths are proportional to the energy; input width = total of the output widths.
  • Extended multi-stage chains (e.g. power station: chemical → internal → kinetic → electrical): the output of one stage is the input to the next.
  • Example: battery and lamp: chemical store → electrical work → light (waves) + internal (heating).
  • Extended falling with no air resistance: loss in Ep = gain in Ek, so mgΔh = ½mv2.
  • Extended doubling the speed quadruples Ek; doubling the mass doubles it.
100 J electrical useful: 70 J kinetic wasted: 30 J (heating, sound) efficiency = 70%
Extended: Sankey diagram for a motor: 100 J in, 70 J useful kinetic, 30 J wasted. Widths match the energies.
Δh top: Ep = mgΔh, Ek = 0 halfway: half and half bottom: Ek = ½mv² = mgΔh
Extended: a falling ball (no air resistance). Ep lost = Ek gained; the total stays mgΔh.

Watch out!

  • Energy is never "used up" or "lost": it is transferred, often to the surroundings.
  • Extended: only the speed is squared in Ek = ½mv2; square v before multiplying.

1.7bWork

Definitions

Work done
the product of the force and the distance moved in the direction of the force.
Work done (energy view)
the energy transferred by a force (mechanical work) or by an electric current (electrical work).
Joule
the work done when a force of 1 N moves its point of application 1 m in the direction of the force.

Key points

  • Work done = energy transferred, measured in joules (1 J = 1 N m).
  • No movement in the direction of the force means no work (e.g. holding a heavy bag still).
  • Lifting at steady speed: force = weight, so work done = mg × height = gain in Ep.
  • Work done against friction transfers energy to the internal store (heating).
  • Braking car: work done by the brakes = the kinetic energy removed.
F = 50 N d = 4 m startend
Work done = F × d = 50 N × 4 m = 200 J transferred.
F = W = mg W Δh work done= mgΔh= gain in Ep
Lifting at steady speed: the force equals the weight, so W = mgΔh.

Watch out!

  • Use the distance moved in the direction of the force, not any distance in the question.
  • Work and energy are both in joules; power is in watts.

1.7cEnergy resources and efficiency

Definitions

Renewable energy resource
a resource that is replaced naturally and will not run out.
Non-renewable energy resource
a resource that is finite and cannot be replaced once it is used up.
Efficiency
Extended the useful energy (or power) output divided by the total energy (or power) input, often × 100%.

Key points

  • Fossil fuels (coal, oil, gas) and biofuels: burned to boil water in a boiler; steam turns a turbine that drives a generator.
  • Nuclear fission and geothermal (hot rocks) also heat water to make steam for turbines.
  • Hydroelectric dams, tides, waves and wind turn turbines directly.
  • Solar cells convert light directly to electricity; solar panels heat water.
  • Compare resources on renewability, availability, reliability, scale and environmental impact.
  • Efficiency (qualitative): the larger the fraction of the input energy transferred usefully, the more efficient the device.
  • Extended radiation from the Sun is the main source of energy for all these except geothermal, nuclear and tidal.
  • Extended the Sun releases energy by nuclear fusion; research aims to use fusion to generate electricity on a large scale.
fuel burns(heating) boilersteam turbinespins generatorelectrical gridto homes wind, water:turn theturbinedirectly also nuclear and geothermal (heat water)
Thermal power station: fuel heats water, steam turns the turbine, the generator produces electricity.
Sun nuclear fusion fossil fuels biofuels wind waves hydroelectric solar not the Sun: geothermal nuclear tidal
Extended: most resources trace back to the Sun. Geothermal, nuclear and tidal do not.

Watch out!

  • Solar cells make electricity; solar panels heat water. Do not swap them.
  • Efficiency can never exceed 100%, and it has no unit.
  • Renewable does not mean reliable: wind and solar depend on the weather.

1.7dPower

Definitions

Power
the work done per unit time, or the energy transferred per unit time.
Watt
a power of one joule per second.

Key points

  • 1 W = 1 J/s; 1 kW = 1000 W.
  • More powerful = does the same work in less time (or more work in the same time).
  • Stair-climb power: measure mass, vertical height of the stairs and time; P = mgh / t.
  • On an energy-time graph, gradient = power.
E / Jt / s high power low power gradient = P
Energy transferred against time: the steeper line is the more powerful machine (gradient = power).
Δh P = mgΔh / t
Stair climb: power = gain in Ep / time = mgΔh / t.

Watch out!

  • Time must be in seconds: 2 minutes = 120 s.
  • Use the vertical height of the stairs, not the length along the slope.

1.8aPressure on surfaces

Definitions

Pressure
the force per unit area.
Pascal (Pa)
a pressure of one newton per square metre.

Key points

  • Same force on a smaller area gives a larger pressure.
  • High pressure (small area): knife blades, drawing pins, nails, stiletto heels.
  • Low pressure (large area): snowshoes, wide tractor tyres, building foundations, camel feet.
  • Pressure increases with force and decreases with area.
  • Area conversions: 1 m2 = 10 000 cm2.
20 N 20 N A = 0.02 m² p = 1000 Pa A = 0.005 m² p = 4000 Pa
The same 20 N brick: lying flat it spreads the force; standing on end the pressure is four times larger.

Watch out!

  • Area in cm2 must be converted to m2 (divide by 10 000) to get pascals.
  • Mass in kg is not force: find the weight (W = mg) first.

1.8bPressure in liquids

Definitions

Pressure in a liquid
the pressure caused by the weight of liquid above a point; it acts equally in all directions.

Key points

  • Pressure beneath a liquid surface increases with depth.
  • At the same depth, pressure is greater in a denser liquid.
  • At a given depth pressure acts equally in all directions and does not depend on the container's shape.
  • Dams are thicker at the bottom; water spurts furthest from the lowest hole in a can.
  • Extended the change in pressure between two depths is Δp = ρgΔh.
greater depth, greater pressure furthest water
Water spurts furthest from the lowest hole, where the pressure is greatest.
surface density ρ Δh Δp = ρgΔh
Extended: pressure arrows grow with depth. The extra pressure over a depth Δh is ρgΔh.

Watch out!

  • Extended: ρgΔh is only the pressure due to the liquid; the total also includes atmospheric pressure on the surface.
  • Extended: Δh is the vertical depth, not the distance along a sloping pipe.
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