Motion, Forces and Energy

• The one sentence that unlocks the chapter: a resultant force does not keep an object moving — it changes how the object is moving. Everything else in Topic 1 is a way of measuring that change: as an acceleration, as a change of momentum, as a transfer of energy, or as a turning effect.
• Section 1.1 in one line: choose the instrument for the size of the reading, remove systematic errors by correction rather than repetition, make small quantities big by measuring multiples, and decide before you write anything whether the answer needs a direction. Mastery check: can you name all six scalars and all eight vectors of this syllabus from memory?
• Section 1.2 in one line: label the axes before you read anything; then gradient means speed on the first graph and acceleration on the second, and area means distance only on the second. Mastery check: can you say what a horizontal line means on each graph without hesitating?
• Section 1.3 in one line: mass in kilograms counts the matter and never changes; weight in newtons is the pull on that matter and follows \(g\) wherever the object goes. Mastery check: can you say which instrument measures which, and why the beam balance is the odd one out?
• Section 1.4 in one line: density is a property of the material, so the mass always comes from a balance and only the route to the volume changes — multiply the dimensions, measure the rise, or subtract two weighings. Mastery check: can you convert \(\mathrm{g/cm^3}\) to \(\mathrm{kg/m^3}\) in the right direction without hesitating?
• Section 1.5 in one line: forces change motion (\(F = ma\)), change shape (\(F = kx\)), change rotation (moment \(=\) force \(\times\) perpendicular distance) and decide whether an object stands or falls (weight line inside or outside the base). Mastery check: can you give the five-step terminal-velocity explanation and the toppling condition without notes?
• Section 1.6 in one line: write the positive direction down first, then total momentum before equals total momentum after — and remember that force is what you get when you divide that change by the time it took. Mastery check: can you explain an airbag without ever saying it “reduces the momentum”?
• Section 1.7 in one line: energy is never lost, only moved to a less useful store; efficiency says what fraction went where you wanted; and power says how quickly the whole transfer happened. Mastery check: can you name all seven stores, all four pathways and all nine energy resources from memory?

• I can describe how to measure a range of lengths with appropriate precision using a tape, a rule and an analogue micrometer, including reading the micrometer scale. 1.1.1
• I can describe how to use a measuring cylinder to find the volume of a liquid, and how to find the volume of a solid by displacement. 1.1.2
• I can describe how to measure a variety of time intervals using clocks and digital timers. 1.1.3
• I can determine an average value for a small distance and for a short time interval by measuring multiples, including the period of a pendulum. 1.1.4
• I can state that a scalar has magnitude only while a vector has magnitude and direction. 1.1.5
• I can name distance, speed, time, mass, energy and temperature as scalars. 1.1.6
• I can name displacement, force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength as vectors. 1.1.7
• I can determine the resultant of two vectors at right angles, by calculation and by scale drawing. 1.1.8
• I can define speed as distance travelled per unit time and velocity as change in displacement per unit time. 1.2.1
• I can recall and use \(v = s/t\). 1.2.2
• I can recall and use average speed \(=\) total distance travelled \(/\) total time taken. 1.2.3
• I can define acceleration as change in velocity per unit time and use \(a = \Delta v/\Delta t\). 1.2.4
• I can state what uniform and non-uniform acceleration mean and describe examples of each. 1.2.5
• I can treat a deceleration as a negative acceleration and use that in calculations. 1.2.6
• I can sketch, plot and interpret distance–time and speed–time graphs. 1.2.7
• I can read from the shape of a distance–time graph whether an object is at rest, at constant speed, accelerating or decelerating. 1.2.8
• I can read from the shape of a speed–time graph whether an object is at rest, at constant speed, at constant acceleration or at changing acceleration. 1.2.9
• I can state that the acceleration of free fall \(g\) near the Earth is approximately constant and approximately \(9.8\ \mathrm{m/s^2}\). 1.2.10
• I can calculate speed from the gradient of a distance–time graph. 1.2.11
• I can calculate distance travelled from the area under a speed–time graph for constant speed or constant acceleration. 1.2.12
• I can calculate acceleration from the gradient of a speed–time graph. 1.2.13
• I can state that mass is a measure of the quantity of matter in an object at rest relative to the observer. 1.3.1
• I can state that the mass of an object resists change from its state of rest or motion, which is inertia. 1.3.2
• I can explain that weights, and therefore masses, may be compared using a beam balance or an equal-arm balance. 1.3.3
• I can describe how to determine mass using an electronic balance. 1.3.4
• I can describe how to measure weight using a force meter. 1.3.5
• I can define gravitational field strength as force per unit mass, use \(g = W/m\), and state that it is equivalent to the acceleration of free fall. 1.3.6
• I can state that a gravitational field is a region in which a mass experiences a force due to gravitational attraction. 1.3.7
• I can define density as mass per unit volume and recall and use \(\rho = m/V\). 1.4.1
• I can describe how to determine the density of a liquid, of a regularly shaped solid and of an irregularly shaped solid that sinks, including the calculations. 1.4.2
• I can identify and use weight, friction, drag, air resistance, tension, electrostatic force, magnetic force, thrust and contact force. 1.5.1.1
• I can identify the forces acting on an object and draw a free-body diagram of them. 1.5.1.2
• I can state the first law of motion: an object remains at rest or continues in a straight line at constant speed unless acted on by a resultant force. 1.5.1.3
• I can state that a force may change the velocity of an object by changing its direction of motion or its speed. 1.5.1.4
• I can determine the resultant of two or more forces acting along the same straight line. 1.5.1.5
• I can recall and use resultant force \(=\) mass \(\times\) acceleration, \(F = ma\). 1.5.1.6
• I can state the third law of motion: when object A exerts a force on object B, object B exerts an equal and opposite force on object A. 1.5.1.7
• I can state that these pairs are forces of the same type acting on different objects. 1.5.1.8
• I can describe friction as a force that may impede motion and produce heating. 1.5.2.1
• I can describe the motion of an object acted on by a constant weight or driving force, with and without drag. 1.5.2.2
• I can explain how an object reaches terminal velocity. 1.5.2.3
• I can define thinking distance, braking distance and stopping distance. 1.5.2.4
• I can explain the factors that affect thinking and braking distance, including speed, tiredness, alcohol, drugs, load, tyre surface and road conditions. 1.5.2.5
• I can state that forces may change the size and shape of an object. 1.5.3.1
• I can define the spring constant as force per unit extension and use \(k = F/x\). 1.5.3.2
• I can sketch, plot and interpret load–extension graphs for an elastic solid and describe the experimental procedure. 1.5.3.3
• I can define and use the term limit of proportionality and identify that point on a load–extension graph. 1.5.3.4
• I can describe qualitatively how speed, radius and mass are related to the size of the force needed for motion in a circular path. 1.5.4.1
• I can describe the moment of a force as a measure of its turning effect and give everyday examples. 1.5.5.1
• I can define and use moment \(=\) force \(\times\) perpendicular distance from the pivot. 1.5.5.2
• I can state and use the principle of moments for an object in equilibrium. 1.5.5.3
• I can describe an experiment to verify the principle of moments. 1.5.5.4
• I can state what is meant by centre of gravity. 1.5.6.1
• I can describe how to find the centre of gravity of a plane lamina using a plumb line. 1.5.6.2
• I can describe qualitatively how the position of the centre of gravity affects the stability of simple objects. 1.5.6.3
• I can define momentum as mass \(\times\) velocity and use \(p = mv\). 1.6.1
• I can define impulse as force \(\times\) time for which the force acts and use impulse \(= F\Delta t = \Delta(mv)\). 1.6.2
• I can apply the principle of conservation of momentum to simple problems in one dimension. 1.6.3
• I can define resultant force as change in momentum per unit time and use \(F = \Delta p/\Delta t\). 1.6.4
• I can state that energy may be stored as kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic and internal (thermal). 1.7.1.1
• I can describe how energy is transferred between stores by forces (mechanical work done), electrical currents (electrical work done), heating, and electromagnetic, sound and other waves. 1.7.1.2
• I can state and apply the principle of the conservation of energy. 1.7.1.3
• I can recall and use \(E_k = \tfrac{1}{2}mv^2\). 1.7.1.4
• I can recall and use \(\Delta E_p = mg\Delta h\). 1.7.1.5
• I can recall and use work done \(=\) force \(\times\) distance moved in the direction of the force, \(W = Fd\). 1.7.2.1
• I can list renewable and non-renewable energy sources. 1.7.3.1
• I can describe how useful energy is obtained, or electrical power generated, from fossil fuels, biofuels, hydroelectric resources, solar radiation, nuclear fuel, geothermal resources, wind, tides and waves in the sea, referring to a boiler, turbine and generator where they are used. 1.7.3.2
• I can describe advantages and disadvantages of each method, limited to whether it is renewable, when and whether it is available, and its impact on the environment. 1.7.3.3
• I can define and use efficiency as useful energy output / total energy input and as useful power output / total power input, with or without the percentage. 1.7.4.1
• I can define power as work done per unit time and as energy transferred per unit time, and use \(P = W/t\) and \(P = \Delta E/t\). 1.7.5.1
• I can define pressure as force per unit area and use \(p = F/A\). 1.8.1
• I can describe how pressure varies with force and area using everyday examples. 1.8.2
• I can state that the pressure at a surface produces a force at right angles to that surface, and describe an experiment to show it. 1.8.3
• I can describe how the height of a liquid column in a liquid barometer is used to determine atmospheric pressure. 1.8.4
• I can describe quantitatively how the pressure beneath a liquid surface changes with depth and with the density of the liquid. 1.8.5
• I can recall and use \(\Delta p = \rho g \Delta h\) for the change in pressure beneath a liquid surface. 1.8.6

Why it matters: momentum questions are almost always sign questions in disguise. Choosing a positive direction, writing it down, and then keeping every velocity consistent with it turns a hard question into arithmetic. Skipping that step is how a collision answer ends up with the wrong magnitude and the wrong direction.

Vector Quantity

A vector quantity is a physical quantity that has both magnitude and direction. Displacement, force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength are vectors, and two vectors at right angles combine to a resultant of magnitude equal to the square root of the sum of their squares.

Acceleration

Acceleration is the change in velocity per unit time, calculated from a = change in velocity divided by time taken. It is a vector measured in metres per second squared, and a negative acceleration relative to the chosen positive direction is a deceleration.

Speed

Speed is the distance travelled per unit time. It is a scalar quantity, measured in metres per second, and is calculated from v = s / t.

Mass

Mass is a measure of the quantity of matter in an object at rest relative to the observer. It is measured in kilograms, is a scalar, and is the property of an object that resists a change from its state of rest or of motion, which is called inertia.

Scalar Quantity

A scalar quantity is a physical quantity that has magnitude (size) only and no direction. Distance, speed, time, mass, energy and temperature are scalars, and they are added by ordinary arithmetic.

Density

Density is the mass per unit volume of a material, calculated from density equals mass divided by volume. It is a scalar measured in kilograms per cubic metre or grams per cubic centimetre, where 1 gram per cubic centimetre equals 1000 kilograms per cubic metre.

Weight

Weight is the gravitational force acting on an object because of its mass. It is a vector measured in newtons, calculated from W = mg, and it changes when the object is moved to a place with a different gravitational field strength.

Resultant Force

The resultant force is the single force that has the same effect as all the forces acting on an object combined. A zero resultant force means the velocity does not change; a non-zero resultant force produces an acceleration given by F = ma in the direction of that resultant.

Inertia

Inertia is the property by which the mass of an object resists a change from its state of rest or of uniform motion. The larger the mass, the larger the force needed to produce a given acceleration.

Velocity

Velocity is the change in displacement per unit time. It is a vector quantity, measured in metres per second, and a complete velocity answer states both a magnitude and a direction.

Hooke's Law

Hooke's law states that the extension of a spring is directly proportional to the load applied, provided the limit of proportionality is not exceeded. It is written F = kx, where k is the spring constant, defined as force per unit extension and measured in newtons per metre.

Moment

The moment of a force is a measure of its turning effect about a pivot, defined as the force multiplied by the perpendicular distance from the pivot to the line of action of the force. It is measured in newton metres.

Momentum

Momentum is defined as mass multiplied by velocity, p = mv. It is a vector measured in kilogram metres per second, so in one dimension it takes the sign of the velocity, and the total momentum of an isolated system is conserved in any interaction.

Centre of Gravity

The centre of gravity of an object is the single point through which the whole weight of the object may be considered to act. For a plane lamina it can be found experimentally by suspending the lamina from two different points in turn and marking the vertical line given by a plumb line each time.

Pressure

Pressure is defined as the force acting per unit area at right angles to a surface, calculated from p = F / A. It is a scalar measured in pascals, where one pascal is one newton per square metre.

Impulse

Impulse is defined as force multiplied by the time for which the force acts, and it is equal to the change in momentum produced. Impulse equals F times delta t equals delta of m v, and it is measured in newton seconds, which are equivalent to kilogram metres per second.

Efficiency

Efficiency is the useful energy output divided by the total energy input, or equivalently the useful power output divided by the total power input, and may be given as a percentage by multiplying by 100. It has no unit and can never exceed 100 per cent.

Power

Power is the work done per unit time, and equivalently the energy transferred per unit time. It is a scalar measured in watts, where one watt is one joule per second, and is calculated from P = W / t or P = change in E / t.

Work

Work done is the energy transferred when a force moves an object, calculated as the force multiplied by the distance moved in the direction of the force. It is a scalar measured in joules, where one joule is one newton metre.

• Error Correction Common-Mistake Clinic Twenty-five statements that sound reasonable and are wrong. Each entry gives the correction, a sentence you can safely write in an answer, and a one-line check. Work through them with the answers covered: if you can produce the correction and the check unprompted, that misconception is fixed. The twenty-five Topic 1 misconceptions #The claim — and why it is wrongThe corrected modelExam-safe sentenceQuick check 1 “Distance and displacement are interchangeable.” They agree only for motion in a straight line without reversing. Distance is the total path length, a scalar. Displacement is the straight-line change in position, a vector with a direction. “The distance travelled is \(14\ \mathrm{km}\), but the displacement is \(10\ \mathrm{km}\) on a bearing of \(037^\circ\).” A runner completes one lap of a \(400\ \mathrm{m}\) track. Distance? Displacement? (\(400\ \mathrm{m}\); zero.) 2 “Speed and velocity mean the same thing.” Everyday speech treats them as synonyms; physics does not. Speed is distance per unit time, a scalar. Velocity is change in displacement per unit time, a vector. “The car travels at a constant speed of \(15\ \mathrm{m/s}\), but its velocity changes because it goes round a bend.” Can an object move at constant speed and still be accelerating? (Yes — if it changes direction.) 3 “Negative acceleration always means slowing down.” The sign refers to a chosen axis, not to speeding up or slowing down. An object slows down when acceleration and velocity have opposite signs. If both are negative, it speeds up in the negative direction. “The acceleration is \(-9.8\ \mathrm{m/s^2}\) throughout, so the ball slows on the way up and speeds up on the way down.” A ball falls with \(a = -9.8\ \mathrm{m/s^2}\) and \(v\) negative. Speeding up or slowing down? (Speeding up.) 4 “A flat distance–time graph means constant speed.” The two motion graphs use the same shape for different meanings. Flat on a distance–time graph means the distance is not changing, so the object is at rest. Flat on a speed–time graph means constant speed. “Between \(10\ \mathrm{s}\) and \(18\ \mathrm{s}\) the distance does not change, so the object is stationary.” What does a horizontal line mean on each of the two graphs? (At rest; constant speed.) 5 “Area under a distance–time graph gives distance.” That area has units of metre-seconds and no physical meaning here. Distance is read directly off the vertical axis of a distance–time graph. Area gives distance only under a speed–time graph. “The distance at \(t = 20\ \mathrm{s}\) is read from the graph as \(40\ \mathrm{m}\).” Multiply the axis units of a distance–time graph together. Is the result a quantity you use? (m s — no.) 6 “Zero resultant force means no forces act.” Balanced is not the same as absent. A zero resultant means the forces present cancel. A book on a table has two forces of equal size acting on it. “The forces are balanced, so the resultant force is zero and the velocity does not change.” How many forces act on a book resting on a table? (Two: weight and contact force.) 7 “A moving object needs a forward resultant force.” This is the pre-Newtonian intuition that motion needs a cause. A resultant force is needed to change motion, not to maintain it. At constant velocity the resultant is zero. “The driving force equals the resistive forces, so the resultant force is zero and the car travels at constant speed.” What is the resultant force on a parachutist at terminal velocity? (Zero.) 8 “Mass and weight use the same unit.” Everyday language says “a kilogram in weight”. Mass is in kilograms; weight is a force in newtons. They are linked by \(W = mg\) but are different quantities. “The mass is \(2.5\ \mathrm{kg}\) and the weight is \(24.5\ \mathrm{N}\).” Give the unit of each. (kg; N.) 9 “Mass changes on the Moon.” It confuses the pull of gravity with the matter present. Mass measures the quantity of matter and is unchanged. Only the weight changes, because \(g\) is smaller. “The mass is unchanged at \(2.5\ \mathrm{kg}\); the weight falls from \(24.5\ \mathrm{N}\) to \(4.0\ \mathrm{N}\) because \(g\) is smaller.” An astronaut floats in orbit. Has their mass changed? (No — they are in continuous free fall.) 10 “Heavy objects always fall faster.” True for a feather and a hammer in air, and false for both in a vacuum. With air resistance negligible, \(a = W/m = mg/m = g\): the mass cancels, so all objects accelerate equally. Differences in air come from drag, not from weight. “Both balls have the same acceleration \(g\), because the mass cancels in \(a = mg/m\).” Why do a coin and a feather land together in an evacuated tube? (No air resistance, so only weight acts and \(a = g\) for both.) 11 “Heavy objects always sink.” A steel ship weighs thousands of tonnes and floats. Whether an object floats depends on its average density compared with that of the liquid, not on its weight. “The stone sank, so its density must be greater than \(1000\ \mathrm{kg/m^3}\).” Why does a steel ship float? (Its average density, including the enclosed air, is less than that of water.) 12 “Friction is always unwanted.” Without it you could not walk, drive, brake or tie a knot. Friction is useful in brakes, tyres, shoes, knots and screws, and unwanted in bearings and engines where it wastes energy by heating. “Friction between the tyres and the road is what provides the force that accelerates and steers the car.” Name one useful and one unwanted effect of friction. (Brakes work; engine parts wear and heat.) 13 “Friction always opposes an object's overall motion.” It opposes the relative sliding of the surfaces. A walker's sole tries to slide backwards, so friction on the shoe acts forwards. The same is true of a car's driving wheels. “The tyre pushes backwards on the road, so friction from the road on the tyre acts forwards and drives the car.” Which way does friction act on a walker's shoe? (Forwards.) 14 “The elastic limit and the limit of proportionality are automatically identical.” They are different ideas, and this syllabus requires only one of them. The limit of proportionality is where the load–extension graph stops being a straight line. This syllabus states that an understanding of the elastic limit is not required, so do not use the two terms as synonyms. “Point P is the limit of proportionality, because beyond it the graph is no longer a straight line.” Which point does the syllabus ask you to identify on a load–extension graph? (The limit of proportionality.) 15 “The extension is the length of the stretched spring.” A frequent slip that makes every spring constant wrong. Extension \(=\) stretched length \(-\) original unloaded length. “\(x = 23.0 - 15.0 = 8.0\ \mathrm{cm}\), so \(k = 4.0/0.080 = 50\ \mathrm{N/m}\).” Which reading must you take before adding any load? (The unloaded length.) 16 “An outward force keeps an object moving in a circle.” The sensation of being thrown outwards is real; the outward force is not. The resultant force acts towards the centre, perpendicular to the velocity. Remove it and the object continues along the tangent. “The tension provides a resultant force towards the centre, which changes the direction of the velocity but not its magnitude.” The string breaks. Which way does the ball go? (Straight on, along the tangent.) 17 “Moment uses the distance to the force arrow.” It uses the perpendicular distance to the line of action. Extend the force's line of action and measure the perpendicular distance from the pivot to that line. If the line passes through the pivot, the moment is zero. “Moment \(=\) force \(\times\) perpendicular distance from the pivot to the line of action of the force.” Why does pushing a door at the hinge not open it? (The perpendicular distance is zero.) 18 “A low centre of gravity alone guarantees stability.” A coin on its edge has a low centre of gravity and falls over instantly. Stability depends on both the height of the centre of gravity and the width of the base: together they decide how far the object must tilt before the weight line leaves the base. “The wider base and lower centre of gravity together mean the bus must tilt much further before it topples.” Name the two design changes that make a vehicle more stable. (Lower centre of gravity; wider wheelbase.) 19 “Momentum is conserved for each object separately.” Each object's momentum usually changes a great deal. The total momentum of the isolated system is conserved. What one object loses, the other gains. “Total momentum before \(=\) total momentum after, because no external resultant force acts on the system.” Trolley A loses \(0.72\ \mathrm{kg\,m/s}\). What does B gain? (\(0.72\ \mathrm{kg\,m/s}\).) 20 “Momentum conservation means kinetic energy is conserved.” Two different quantities obeying two different rules. Momentum is conserved in every isolated-system collision. Kinetic energy is conserved only in a perfectly elastic one, and never when objects stick together or deform. “Momentum is conserved; kinetic energy is not, because some is transferred to internal energy and sound as the trolleys deform.” Two trolleys stick together. Is kinetic energy conserved? (No.) 21 “Airbags reduce the momentum change.” The passenger stops either way, so \(\Delta p\) is fixed by the crash. The airbag increases the time over which the momentum change happens, and \(F = \Delta p/\Delta t\) then gives a smaller average force. “The airbag increases the time taken to stop, so for the same change of momentum the average force on the passenger is smaller.” \(\Delta p = 1500\ \mathrm{kg\,m/s}\) in \(0.020\ \mathrm{s}\), then in \(0.20\ \mathrm{s}\). Compare the forces. (\(75\,000\ \mathrm{N}\); \(7500\ \mathrm{N}\).) 22 “Energy is used up.” Conservation of energy says the total never changes. Energy is transferred and dissipated, never destroyed. “Wasted” energy has moved to a less useful store, usually the internal energy of the surroundings. “The energy has been transferred to the internal energy of the brakes and the surrounding air, and to sound.” Where is the energy after a bouncing ball stops? (Internal energy of ball, floor and air, plus sound.) 23 “Power and energy are the same.” One says how much, the other how fast. Energy is measured in joules; power is the rate of transfer, measured in watts, where \(1\ \mathrm{W} = 1\ \mathrm{J/s}\). “Both motors do \(1200\ \mathrm{J}\) of work, but the one that takes \(3.0\ \mathrm{s}\) has four times the power of the one that takes \(12\ \mathrm{s}\).” Give the unit of each. (J; W.) 24 “Efficiency can exceed 100%.” That would mean creating energy. The useful output is only part of the total input, and by conservation the outputs sum to the input, so the ratio cannot exceed \(1\). “Efficiency \(= 9/60 = 0.15\), which is \(15\%\).” A calculation gives \(667\%\). What has gone wrong? (The fraction is upside down.) 25 “Renewable energy has no environmental impact.” Renewable describes the supply, not the impact. Every resource has some impact: dams flood valleys, turbines occupy land and affect birds, barrages alter estuaries, and panels must be manufactured and disposed of. “Wind is renewable and releases no combustion products in use, but the turbines have a visual and noise impact and the output cannot be scheduled.” Name one environmental drawback of hydroelectric power. (A valley is flooded, destroying habitats.) Two more, on pressure — the pair that most often appear together The claim — and why it is wrongThe corrected modelExam-safe sentenceQuick check “A larger area produces a larger pressure for the same force.” The relationship is inverted: \(p = F/A\). With the force fixed, a larger area gives a smaller pressure. That is exactly why snowshoes, skis and wide tyres work, and why a drawing pin has a point. “The weight is unchanged but the contact area is larger, so the pressure on the snow is smaller and the wearer does not sink in.” Flat shoes or stilettos: which gives the greater pressure on a floor? (Stilettos — far smaller area.) “Liquid pressure depends on the shape of the container.” \(\Delta p = \rho g \Delta h\) contains no width, area or volume. Only the vertical depth and the density matter. A wide tank has a greater total force on its base than a narrow tube, but only because the base has a larger area — the pressure at a given depth is identical. “The pressure depends only on the depth and the density of the liquid, so it is the same at that level in all three vessels.” Two connected vessels of different width hold water. At what levels does it settle? (The same level in both.) How to use this clinic: cover the right-hand three columns and read only the claim. If you can produce the correction, the exam-safe sentence and the check from memory, move on. If you cannot, go back to the section that teaches it — re-reading the correction alone does not fix a misconception, retrieving it does.

• What this checklist deliberately does not contain Three ideas that often appear in general physics resources are not printed anywhere in Topic 1 of this syllabus, and are therefore treated here as clearly labelled enrichment rather than as requirements: the circular-motion equation \(F = mv^2/r\) (the syllabus states explicitly that it is not required), the elastic limit as distinct from the limit of proportionality (the syllabus states explicitly that an understanding of the elastic limit is not required), and hydraulic machines and the flotation condition. Where they appear on this page they carry an Extension badge.
• Choosing the cylinder, not just reading it A \(100\ \mathrm{cm^3}\) cylinder graduated in \(1\ \mathrm{cm^3}\) is the right choice for a \(60\ \mathrm{cm^3}\) sample. A \(1000\ \mathrm{cm^3}\) cylinder graduated in \(10\ \mathrm{cm^3}\) is not, because the same \(60\ \mathrm{cm^3}\) is then known only to the nearest \(5\ \mathrm{cm^3}\). Use the smallest cylinder the sample will fit into, and say so if the question asks you to justify your apparatus.
• Average speed is not the average of the speeds If a journey has two stages at \(20\ \mathrm{m/s}\) and \(30\ \mathrm{m/s}\), the average speed is \(25\ \mathrm{m/s}\) only if the two stages take the same time. If instead the two stages cover the same distance, the slower stage takes longer and the average speed is \(24\ \mathrm{m/s}\), not \(25\). And if the journey includes a stop, the stopped time still counts in the total time. Always go back to total distance divided by total time.
• How this syllabus limits the evaluation — and why that helps you The printed statement restricts the advantages and disadvantages to three things only: whether the resource is renewable, when and whether it is available, and its impact on the environment. Answer within those three headings and you will not run out of relevant points. Two cautions follow from that wording. First, renewable does not mean impact-free: a hydroelectric dam floods a valley, wind turbines affect birds and landscape, and every solar panel has to be manufactured and eventually disposed of. Write “lower environmental impact in use” rather than “no environmental impact”. Second, keep physics separate from economics and geography. “Geothermal energy requires hot rock near the surface” is a physical constraint. “Geothermal is cheap” is a claim about cost that depends entirely on location and date, and is not physics. Mark yourself down for any sentence you could not defend without knowing which country you are in.
• The five questions every practical answer must answer What did you change? (independent variable) — exactly one thing. What did you measure? (dependent variable) — with what instrument, to what resolution. What did you keep the same? (controlled variables) — this is where the fair-test marks live. How did you improve reliability? — repeats and a mean, a wide range of values, a best-fit line. Why might the answer be wrong, and in which direction? — say whether the error makes the result too large or too small, not merely “inaccurate”. Improvements that earn nothing: “be more careful”, “use better equipment”, “do it more accurately”, “repeat the experiment” on its own. An improvement must name a specific change and say what it fixes: “use a light gate instead of a stopwatch, because human reaction time is comparable with the interval being timed”.
• The four symbol clashes to read from context \(W\) — weight in newtons (section 1.3) or work done in joules (section 1.7). \(p\) — momentum in kg m/s (section 1.6) or pressure in Pa (section 1.8). \(g\) — the acceleration of free fall in \(\mathrm{m/s^2}\) or the gravitational field strength in N/kg. Same number, two names, two units. \(v\) and \(u\) — used for both speed (scalar) and velocity (vector). Whether a direction is needed depends on the question, not on the letter. The unit is what disambiguates every one of these, which is the practical reason for the rule that every numerical answer carries its unit.
• Drawing a graph that scores Axes: label each as quantity / unit, for example speed / (m / s). The slash means “divided by”, so the numbers on the axis are pure numbers. Scale: choose one so the plotted points occupy more than half the grid in both directions, and use sensible intervals (\(1\), \(2\), \(5\) or \(10\) per square) that you can read between. Points: small, neat crosses or dots in circles — not blobs. Line: a thin best-fit straight line or a smooth curve, with roughly equal numbers of points either side. Never join the points dot to dot. Anomalies: circle a clear outlier and ignore it when drawing the line, but say in words that you have done so and why. Origin: include it only if the theory predicts the line passes through it, or if the data reaches that far. A forced origin can hide a systematic error.
• Phrases that lose marks, and the versions that do not Rewrite these on sight AvoidWrite instead “energy is lost”“energy is transferred to the internal energy store of the surroundings” “there is no force” (at terminal velocity)“the forces are balanced, so the resultant force is zero” “gravity pulls it down”“the weight of the object acts vertically downwards” “it goes faster because there is more force”“the resultant force increases, so by \(F = ma\) the acceleration increases” “the reading is inaccurate”“the reading is too large, because the trapped air bubble increases the measured volume” “be more careful”“use a light gate instead of a stopwatch, because reaction time is comparable with the interval” “repeat the experiment”“take three readings at each load and use the mean, to reduce the effect of random errors” “the graph goes up”“the gradient is constant and positive, so the speed is constant” “it weighs \(5\ \mathrm{kg}\)”“it has a mass of \(5\ \mathrm{kg}\)” or “its weight is \(49\ \mathrm{N}\)” “the force is centrifugal”“the resultant force acts towards the centre of the circle”