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 1.3 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 (Core): can you define gravitational field strength, give its unit, and say what it is equivalent to? Mastery check (Supplement): can you explain a change of weight purely in terms of the field acting on the mass?
• 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 1.8 in one line: pressure is force spread over area, so shrinking the area magnifies the effect; and in a liquid only vertical depth and density matter, never the shape of the container. Mastery check: can you say when \(\rho g \Delta h\) is the whole answer and when atmospheric pressure must be added?
• The practical section in one line: name what you changed, what you measured and what you kept the same; take enough readings across a wide enough range to draw a line; and when you discuss an error, always say which way it pushes the answer. Mastery check: for any of the eleven investigations, can you give one error and state whether it makes the final value too large or too small?
• 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.

• I can describe the use of rulers and measuring cylinders to find a length or a volume, including finding the volume of a solid by displacement. Core 1.1.1
• I can describe how to measure a variety of time intervals using clocks and digital timers. Core 1.1.2
• I can determine an average value for a small distance and for a short interval of time by measuring multiples, including the period of oscillation of a pendulum. Core 1.1.3
• I can define speed as distance travelled per unit time, and recall and use \(v = s/t\). Core 1.2.1
• I can define velocity as speed in a given direction. Core 1.2.2
• I can recall and use average speed \(=\) total distance travelled \(/\) total time taken. Core 1.2.3
• I can sketch, plot and interpret distance–time and speed–time graphs. Core 1.2.4
• I can determine, qualitatively, from given data or the shape of a distance–time or speed–time graph, when an object is at rest, moving with constant speed, accelerating or decelerating. Core 1.2.5
• I can calculate speed from the gradient of a straight-line section of a distance–time graph. Core 1.2.6
• I can calculate the area under a speed–time graph to determine the distance travelled, for motion with constant speed or constant acceleration. Core 1.2.7
• I can state that the acceleration of free fall \(g\) for an object near the surface of the Earth is approximately constant and approximately \(9.8\ \mathrm{m/s^2}\). Core 1.2.8
• I can state that mass is a measure of the quantity of matter in an object at rest relative to the observer. Core 1.3.1
• I can state that weight is a gravitational force on an object that has mass. Core 1.3.2
• I can define gravitational field strength as force per unit mass, recall and use \(g = W/m\), and know that this is equivalent to the acceleration of free fall. Core 1.3.3
• I can state that weights, and therefore masses, may be compared using a balance. Core 1.3.4
• I can define density as mass per unit volume, and recall and use \(\rho = m/V\). Core 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 which sinks in a liquid (volume by displacement), including the appropriate calculations. Core 1.4.2
• I can determine whether an object floats, based on density data. Core 1.4.3
• I can state that forces may produce changes in the size and shape of an object. Core 1.5.1.1
• I can sketch, plot and interpret load–extension graphs for an elastic solid, and describe the associated experimental procedures. Core 1.5.1.2
• I can determine the resultant of two or more forces acting along the same straight line. Core 1.5.1.3
• I can state that an object either remains at rest or continues in a straight line at constant speed unless acted on by a resultant force. Core 1.5.1.4
• I can state that a resultant force may change the velocity of an object by changing its direction of motion or its speed. Core 1.5.1.5
• I can describe solid friction as the force between two surfaces that may impede motion and produce heating. Core 1.5.1.6
• I can state that friction (drag) acts on an object moving through a liquid. Core 1.5.1.7
• I can state that friction (drag) acts on an object moving through a gas, for example air resistance. Core 1.5.1.8
• I can describe the moment of a force as a measure of its turning effect, and give everyday examples. Core 1.5.2.1
• I can define the moment of a force as force \(\times\) perpendicular distance from the pivot, and recall and use this equation. Core 1.5.2.2
• I can apply the principle of moments to situations with one force each side of the pivot, including the balancing of a beam. Core 1.5.2.3
• I can state that, when there is no resultant force and no resultant moment, an object is in equilibrium. Core 1.5.2.4
• I can state what is meant by centre of gravity. Core 1.5.3.1
• I can describe an experiment to determine the position of the centre of gravity of an irregularly shaped plane lamina. Core 1.5.3.2
• I can describe, qualitatively, the effect of the position of the centre of gravity on the stability of simple objects. Core 1.5.3.3
• I can state that energy may be stored as kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic and internal (thermal). Core 1.7.1.1
• I can describe how energy is transferred between stores during events and processes, including transfer by forces (mechanical work done), by electrical currents (electrical work done), by heating, and by electromagnetic, sound and other waves. Core 1.7.1.2
• I can state the principle of the conservation of energy and apply it to simple examples, including the interpretation of simple flow diagrams. Core 1.7.1.3
• I can explain that mechanical or electrical work done is equal to the energy transferred. Core 1.7.2.1
• I can recall and use the equation for mechanical working, \(W = Fd = \Delta E\). Core 1.7.2.2
• I can describe how useful energy may be obtained, or electrical power generated, from chemical energy stored in fossil fuels and in biofuels; from water, including waves, tides and water behind hydroelectric dams; from geothermal resources; from nuclear fuel; from light from the Sun using solar cells; and from infrared and other electromagnetic waves from the Sun, which heat water in solar panels and are the source of wind energy — including references to a boiler, turbine and generator where they are used. Core 1.7.3.1
• I can describe advantages and disadvantages of each method in terms of renewability, availability, reliability, scale and environmental impact. Core 1.7.3.2
• I can explain, qualitatively, the concept of efficiency of energy transfer. Core 1.7.3.3
• I can define power as work done per unit time and also as energy transferred per unit time, and recall and use \(P = W/t\) and \(P = \Delta E/t\). Core 1.7.4.1
• I can define pressure as force per unit area, and recall and use \(p = F/A\). Core 1.8.1
• I can describe how pressure varies with force and area in the context of everyday examples. Core 1.8.2
• I can describe, qualitatively, how the pressure beneath the surface of a liquid changes with the depth and with the density of the liquid. Core 1.8.3
• I can explain that a scalar quantity has magnitude (size) only and that a vector quantity has magnitude and direction. Supplement 1.1.4
• I can name distance, speed, time, mass, energy and temperature as scalars. Supplement 1.1.5
• I can name force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength as vectors. Supplement 1.1.6
• I can determine, by calculation or graphically, the resultant of two vectors at right angles, limited to forces or velocities only. Supplement 1.1.7
• I can define acceleration as change in velocity per unit time, and recall and use \(a = \Delta v/\Delta t\). Supplement 1.2.9
• I can determine from given data or the shape of a speed–time graph when an object is moving with constant acceleration and when with changing acceleration. Supplement 1.2.10
• I can calculate acceleration from the gradient of a speed–time graph. Supplement 1.2.11
• I can state that a deceleration is a negative acceleration, and use this in calculations. Supplement 1.2.12
• I can describe the motion of objects falling in a uniform gravitational field with and without air or liquid resistance, including reference to terminal velocity. Supplement 1.2.13
• I can describe, and use the concept of, weight as the effect of a gravitational field on a mass. Supplement 1.3.5
• I can determine whether one liquid will float on another liquid, based on density data, given that the liquids do not mix. Supplement 1.4.4
• I can define the spring constant as force per unit extension, and recall and use \(k = F/x\). Supplement 1.5.1.9
• I can define and use the term limit of proportionality for a load–extension graph, and identify this point on the graph. Supplement 1.5.1.10
• I can recall and use \(F = ma\), and know that the force and the acceleration are in the same direction. Supplement 1.5.1.11
• I can describe, qualitatively, motion in a circular path due to a force perpendicular to the motion: speed increases if force increases with mass and radius constant; radius decreases if force increases with mass and speed constant; and an increased mass requires an increased force to keep speed and radius constant. Supplement 1.5.1.12
• I can apply the principle of moments to other situations, including those with more than one force each side of the pivot. Supplement 1.5.2.5
• I can describe an experiment to demonstrate that there is no resultant moment on an object in equilibrium. Supplement 1.5.2.6
• I can define momentum as mass \(\times\) velocity, and recall and use \(p = mv\). Supplement 1.6.1
• I can define impulse as force \(\times\) time for which the force acts, and recall and use impulse \(= F\Delta t = \Delta(mv)\). Supplement 1.6.2
• I can apply the principle of the conservation of momentum to solve simple problems in one dimension. Supplement 1.6.3
• I can define resultant force as the change in momentum per unit time, and recall and use \(F = \Delta p/\Delta t\). Supplement 1.6.4
• I can recall and use the equation for kinetic energy, \(E_k = \tfrac{1}{2}mv^2\). Supplement 1.7.1.4
• I can recall and use the equation for the change in gravitational potential energy, \(\Delta E_p = mg\Delta h\). Supplement 1.7.1.5
• I can apply the principle of the conservation of energy to complex examples involving multiple stages, including the interpretation of Sankey diagrams. Supplement 1.7.1.6
• I can state that radiation from the Sun is the main source of energy for all our energy resources except geothermal, nuclear and tidal. Supplement 1.7.3.4
• I can state that energy is released by nuclear fusion in the Sun. Supplement 1.7.3.5
• I can state that research is being carried out to investigate how energy released by nuclear fusion can be used to produce electrical energy on a large scale. Supplement 1.7.3.6
• I can define efficiency as useful energy output \(/\) total energy input and as useful power output \(/\) total power input, with or without the percentage, and recall and use both equations. Supplement 1.7.3.7
• I can recall and use the equation for the change in pressure beneath the surface of a liquid, \(\Delta p = \rho g \Delta h\). Supplement 1.8.4

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.

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.

Vector Quantity

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

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.

Resultant Force

The resultant force is the single force that has the same effect as all the forces acting on an object combined. Forces acting along the same straight line are combined by adding those in the chosen positive direction and subtracting those in the opposite direction. A zero resultant force means the velocity does not change; a non-zero resultant force changes the object's speed or its direction of motion.

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.

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.

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. In this syllabus acceleration is Supplement content, for Extended candidates.

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.

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.

Velocity

Velocity is speed in a given direction. It is measured in metres per second, and a complete velocity answer states both a magnitude and a direction.

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. Mechanical or electrical work done is equal to the energy transferred, written W = Fd = change in E. It is a scalar measured in joules, where one joule is one newton metre.

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.

Weight

Weight is a gravitational force on an object that has 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.

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.

Mass

Mass is a measure of the quantity of matter in an object at rest relative to the observer. It is measured in kilograms and does not change when the object is moved to a place with a different gravitational field strength.

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.

• Error Correction Common-Mistake Clinic Twenty-seven 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. Each row carries the tier of the statement it protects. Core candidates can skip a row tagged Supplement only — it guards content that is not on Papers 1 and 3. A row carrying both tags matters to every candidate, and the Supplement half of it is flagged inside the row. Extended candidates need all twenty-seven. The twenty-five Topic 1 misconceptions, tagged by tier #The claim — and why it is wrongThe corrected modelExam-safe sentenceQuick check 1 Core 1.2.3 “Average speed is the average of the speeds.” It is only the mean of the stage speeds when every stage takes the same time, which questions rarely arrange. Average speed is always total distance travelled divided by total time taken. Time spent stopped counts in the total time, and stages that take longer weigh more heavily. “Average speed \(=\) total distance \(/\) total time \(= 2000/620 = 3.2\ \mathrm{m/s}\), which is less than the \(4.0\ \mathrm{m/s}\) of each moving stage because of the rest.” A journey runs \(1200\ \mathrm{m}\) in \(300\ \mathrm{s}\), rests \(120\ \mathrm{s}\), then \(800\ \mathrm{m}\) in \(200\ \mathrm{s}\). Average speed? (\(3.2\ \mathrm{m/s}\), not \(4.0\).) 2 Core 1.2.2 “Speed and velocity mean the same thing.” Everyday speech treats them as synonyms; physics does not. Speed is distance travelled per unit time. Velocity is speed in a given direction, so it is incomplete without one. “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 Supplement 1.2.12 “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 Core 1.2.5 “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 Core 1.2.7 “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 Core 1.5.1.3 “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 Core 1.5.1.4 “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 Core 1.3.2 “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 Core 1.3.1 “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 Core 1.2.8 “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, every object near the Earth’s surface falls with the same acceleration of free fall \(g\), whatever its mass. Differences seen in air come from drag, not from weight. “With air resistance negligible both balls fall with the same acceleration of free fall \(g\), so they land together.” 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 Core 1.4.3 “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 Core 1.5.1.6 “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 Core 1.5.1.6 “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 Supplement 1.5.1.10 “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 Core 1.5.1.2 Supplement 1.5.1.9 “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 Supplement 1.5.1.12 “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 Core 1.5.2.2 “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 Core 1.5.3.3 “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 Supplement 1.6.3 “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 Supplement 1.6.3 “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 Supplement 1.6.4 “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 Core 1.7.1.3 “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 Core 1.7.4.1 “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 Core 1.7.3.3 Supplement 1.7.3.7 “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 Core 1.7.3.2 “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 Core 1.8.1 Core 1.8.2 “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.) Core 1.8.3 Supplement 1.8.4 “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 the tier labels do and do not mean A Supplement block is extra depth on the same physics, not harder wording of Core physics. It is not revision of what you have just read. Being a Core candidate does not mean a reduced practical standard. Papers 5 and 6 assess both routes against the same experimental-skills framework, so every practical section on this page is for everyone. Topic 1 is unusual in one way worth knowing now: momentum and impulse are Supplement in their entirety, and so are \(F = ma\), \(E_k = \tfrac{1}{2}mv^2\), \(\Delta E_p = mg\Delta h\) and \(\Delta p = \rho g \Delta h\). If you are a Core candidate and a question hands you one of those equations, you are looking at an Extended paper.
• About the reference numbers on this page Codes such as Core 1.2.1 and Supplement 1.2.9 are Academiq’s shorthand: the official Cambridge sub-topic number (here 1.2 Motion), followed by the number Cambridge prints beside that statement in the sub-topic’s list. Cambridge does not itself write the code in this joined-up dotted form, so treat it as a navigation aid for finding a statement on this page rather than as Cambridge notation to quote in an examination. Both the tier word in front of it — Core or Supplement — and the numbers themselves are taken directly from the syllabus.
• Where the tier boundary will surprise you Four boundaries in Topic 1 catch candidates out more than any others, because they place familiar equations on the Extended side of the line: Acceleration. Core candidates read acceleration off the shape of a graph — is the object speeding up or slowing down? Defining it, calculating it from \(a = \Delta v/\Delta t\), and taking it from a gradient are all Supplement. \(F = ma\). Core requires that a resultant force changes an object’s speed or direction. The equation linking that force to the acceleration it produces is Supplement. Energy equations. Core requires the stores, the transfers, conservation and simple flow diagrams. \(E_k = \tfrac{1}{2}mv^2\), \(\Delta E_p = mg\Delta h\), Sankey diagrams and the efficiency equations are all Supplement — but \(W = Fd\) and \(P = W/t\) are Core. Momentum. All four statements of sub-topic 1.6 are Supplement. There is no Core momentum.
• What this checklist deliberately does not contain Two ideas that appear in many general physics resources are not printed anywhere in Topic 1 of this syllabus, and the syllabus rules them out by name: the circular-motion equation \(F = mv^2/r\), and the elastic limit as something distinct from the limit of proportionality. Neither is required, and neither is treated as a requirement on this page. Several ideas that other physics courses teach alongside this material are also absent, because the 0625 subject content does not print them for Topic 1: reading an analogue micrometer, free-body diagrams and the named catalogue of force types, the third law of motion and force pairs, inertia as mass resisting a change of motion, thinking, braking and stopping distances, and the liquid barometer. If you have met any of them elsewhere they remain useful background, but they are not examinable content for this syllabus and nothing on this page depends on them.
• 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.
• The five headings the evaluation must use Core 1.7.3.2 The printed statement names five criteria, and a full-mark evaluation works through the ones that apply: Renewability — will the supply run out on a human timescale? Availability — where and when can it be used at all? Geothermal needs hot rock near the surface; hydroelectric needs hills and rainfall. Reliability — can the output be counted on, and can it be scheduled? This is not the same as availability. Tidal energy is highly predictable but still pauses around slack water; wind is available in many places but unreliable hour to hour; nuclear and geothermal run continuously. Scale — how much power can one installation actually deliver? A single nuclear station and a single rooftop solar panel are separated by a factor of about a million, and a sentence that ignores that is not an evaluation. Environmental impact — in construction, in use and in disposal. Two cautions follow. First, renewable does not mean impact-free: a hydroelectric dam floods a valley, wind turbines affect birds and landscape, and every solar cell 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. “Geothermal energy requires hot rock near the surface” is a physical constraint on availability. “Geothermal is cheap” is a claim about cost that depends entirely on location and date, and is not physics.
• 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”