Mass — the quantity of matter, in kilograms
Mass is a measure of the quantity of matter in an object, measured in kilograms (kg). It is also the property that resists a change in motion (its inertia), so an object is just as hard to shake in space as on Earth. Mass does not depend on location: the same object has the same mass on the Earth, on the Moon and in deep space. This is why a beam balance, which compares masses, reads the same wherever it is used.
Weight — the gravitational force, in newtons
Weight is the gravitational force acting on a mass, measured in newtons (N) — never in kilograms. Link to mass: , where is the gravitational field strength, defined as weight per unit mass, , in N/kg. Near the Earth's surface N/kg. Weight follows the local : a 70 kg astronaut weighs 686 N on Earth, 112 N on the Moon ( N/kg) and about 0 N in deep space, so a newton (spring) balance reads less there.
(Extended) g — field strength and free-fall acceleration
Weight is the effect of a gravitational field on a mass: a gravitational field is a region in which any mass experiences a force, and that force is the object's weight, . The same is numerically equal to the acceleration of free fall. For an object falling freely the only force is its weight, so and the mass cancels, leaving . The units agree because N kg m/s, so 1 N/kg is 1 m/s and 9.8 N/kg is 9.8 m/s.
Drawn from real examiner reports.
Weight in kilograms, not newtons
Weight is a force, so it is measured in newtons — writing "weight = 686 kg" scores zero. A supermarket label reading 1 kg gives a mass; the corresponding weight on Earth is N. Keep the pairing sharp: mass goes with quantity of matter and kg, weight goes with gravitational force and N.
Flagged Jun 2022 P42 Q6a; Jun 2023 P11 Q29; Nov 2023 P11 Q28
The unit of g is N/kg
Gravitational field strength is weight per unit mass, so its unit is the newton per kilogram (N/kg) — not N, and not kg. Candidates routinely muddle the three units of this topic, quoting in newtons or a weight in N/kg. Write N/kg on Earth, and check any you calculate comes out in N/kg.
Flagged Jun 2022 P42 Q6a; Jun 2023 P11 Q29; Nov 2023 P11 Q28
Inverting g = W/m into m/W
Gravitational field strength is weight divided by mass, . Writing gives the wrong value and the unit kg/N. Unit-check it: the answer must be N (weight) divided by kg (mass), giving N/kg. An inverted formula reads as perfectly plausible on the page, so re-derive it rather than trusting a remembered version.
Rearranging W = mg the wrong way
To find a mass from a weight you divide: . Writing multiplies where you should divide, and gives neither the right number nor kilograms. Check the units: N divided by N/kg gives kg. Rearrange one step at a time from the base equation instead of quoting a half-remembered rearranged form.
Assuming weight is the same everywhere
Only mass is unchanged by location. Weight depends on the local gravitational field strength, so a 25 kg crate weighs 245 N on Earth but only 40 N on the Moon, where N/kg. Saying an astronaut's weight is the same on the Moon — or that their mass falls there — reverses the two quantities and loses the mark.
Using a weight where a mass is needed
Everyday speech uses "weight" for both quantities, so candidates substitute one for the other. If a question quotes a weight in newtons but the physics needs a mass in kilograms — for example before using — convert first with . Putting newtons where kilograms belong is wrong both numerically and dimensionally.
"Heaviness" defines neither quantity
"How heavy something is" earns nothing for either term, and "the pull of gravity" is not enough for weight. The mark-scheme forms are: weight is the gravitational force acting on a mass, in newtons; mass is the quantity of matter in an object, in kilograms. Learn both wordings verbatim — this is a definition-precision mark.
Equation, then substitution, then unit
Write the equation first ( or ), rearrange one step at a time, substitute the numbers, then give the answer with its unit — N for weight, kg for mass, N/kg for . Usually 2-mark items: one mark for the substitution, one for the value with its unit.
Unit-check before you move on
A unit check catches an inverted rearrangement before it costs marks. Weight must come out in N, mass in kg and field strength in N/kg. If your working produces kg/N, you have divided the wrong way round — go back to the base equation and rearrange again.
Use g = 9.8 N/kg unless told otherwise
0654 uses N/kg near the Earth's surface — do not round it to 10. If the question supplies a different value, such as 1.6 N/kg on the Moon or a figure for another planet, use the value given rather than the Earth one.
Weight-mass graph: gradient, not area
On a graph of weight (y-axis) against mass (x-axis), is the gradient of the best-fit straight line through the origin — not the area beneath it, and not mass divided by weight. Label both axes with quantity and unit (W / N and m / kg) and take the gradient from a large triangle.
Cambridge 0654 spec reference: Section P1 "Motion, forces and energy", sub-topic P1.3 "Mass and weight" (Core + Extended combined, single tier). This leaf covers what mass and weight are, the difference between them, gravitational field strength (about 9.8 N/kg near the Earth's surface), and the Extended idea that weight is the effect of a gravitational field and that equals the acceleration of free fall.
Out of scope for P1.3 (covered by later leaves): density (P1.4); resultant force and calculations, friction and springs (P1.5); orbital field-strength variation (P6). Momentum is out of scope for 0654 entirely.
where
(E) The units N/kg and m/s are equivalent, so the gravitational field strength ( in N/kg) is numerically the same as the acceleration of free fall ( in m/s).
Which equation correctly defines the gravitational field strength ?
A B C D
(a) Define mass and state its unit. (1 mark)
(b) Define weight and state its unit. (1 mark)
(c) State one way in which mass and weight differ. (1 mark)
