Units, Measurement & Error Analysis – Review Flashcards

Flashcards covering key concepts from Units & Measurement, dimensional analysis, astronomical distances, SI conventions, and error propagation.

What is a physical quantity?

A measurable property of a phenomenon used to explain physical changes and express laws, e.g., length, mass, time.

How does a vector quantity differ from a scalar quantity?

A vector has both magnitude and direction, while a scalar has magnitude only.

What does ‘magnitude’ refer to in physics?

The size, amount, or numerical value of a physical property without considering direction.

Define a fundamental physical quantity.

A quantity that does not depend on any other physical quantity for its measurement.

List the seven SI fundamental quantities with their units.

Length-metre (m), Mass-kilogram (kg), Time-second (s), Temperature-kelvin (K), Electric current-ampere (A), Luminous intensity-candela (cd), Amount of substance-mole (mol).

What is a derived quantity?

A quantity that depends on fundamental quantities and can be expressed in terms of them, e.g., velocity, force.

Give the SI derived unit for velocity.

Metre per second (m s⁻¹).

State the SI derived unit for force.

Newton (N) = kg m s⁻².

Name the three common systems of units before SI.

MKS (metre-kilogram-second), CGS (centimetre-gram-second), FPS (foot-pound-second).

What are the SI supplementary units?

Plane angle (radian, rad) and solid angle (steradian, sr).

Define a radian.

Plane angle subtended at a circle’s centre by an arc equal in length to the radius (1 rad ≈ 57.297°).

Define a steradian.

Solid angle that, subtended at the centre of a sphere, cuts off an area on the surface equal to the square of the radius (maximum 4π sr for a sphere).

Give the SI prefixes for 10³, 10⁶ and 10⁹.

Kilo (k), mega (M), giga (G).

Give the SI prefixes for 10⁻³, 10⁻⁶ and 10⁻⁹.

Milli (m), micro (µ), nano (n).

State two capitalization rules for SI unit symbols.

Unit names are in lowercase even if named after a person (newton), but symbols begin with a capital letter if derived from a name (N).

Should SI unit symbols be pluralised or end with a period?

No; symbols never take plural form or a full stop (e.g., 20 N, not 20 Ns or 20 newtons.).

Write acceleration correctly using SI notation.

a = m s⁻² (or m/s²), not m/s/s.

What is parallax?

The apparent change in an object’s position due to a change in the observer’s viewpoint.

Formula to find stellar distance by parallax (small angle).

D ≈ b/θ, where b is baseline (e.g., 1 AU) and θ is parallax angle in radians.

Define an astronomical unit (AU).

Mean distance between Earth’s centre and the Sun’s centre ≈ 1.496 × 10¹¹ m.

Define a light-year and give its value in metres.

Distance light travels in one year ≈ 9.46 × 10¹⁵ m.

Define a parsec and express it in light-years.

Distance at which 1 AU subtends an angle of 1″; 1 pc ≈ 3.08 × 10¹⁶ m ≈ 3.26 ly.

Convert 1° into radians.

1° = 1.745 × 10⁻² rad.

State the dimensional formula of density ρ.

[M L⁻³].

State the dimensional formula of acceleration a.

[L T⁻²].

State the dimensional formula of momentum p.

[M L T⁻¹].

State the dimensional formula of work/energy.

[M L² T⁻²].

Give two main uses of dimensional analysis.

(1) Check the dimensional correctness of equations, (2) derive relations or conversion factors between units.

List two limitations of dimensional analysis.

Cannot determine dimensionless constants; not applicable to equations with trigonometric, exponential or logarithmic functions.

Convert 1 Joule to ergs.

1 J = 10⁷ erg.

What is a fermi (fm)?

A length of 10⁻¹⁵ m, often used for nuclear dimensions.

What is an angstrom (Å)?

A length of 10⁻¹⁰ m, used for atomic-scale distances.

Define the atomic mass unit (u).

1/12 of the mass of an unexcited carbon-12 atom ≈ 1.66054 × 10⁻²⁷ kg.

What is absolute error?

The magnitude of the difference between an individual measurement and the true (or mean) value.

How is arithmetic mean calculated?

Σxᵢ / n, where xᵢ are observations and n is their number.

Define relative error.

Absolute error divided by the true (mean) value.

Define percentage error.

Relative error × 100%.

Give the absolute error in the sum Z = A + B.

ΔZ = ΔA + ΔB.

Give the absolute error in the difference Z = A − B.

ΔZ = ΔA + ΔB (errors always add for worst-case estimate).

Express fractional error in a product Z = AB.

ΔZ/Z = ΔA/A + ΔB/B.

Express fractional error in a quotient Z = A/B.

ΔZ/Z = ΔA/A + ΔB/B.

Express fractional error for a power Z = Aⁿ.

ΔZ/Z = n (ΔA/A).

Summarise error propagation rules for (a) addition/subtraction, (b) multiplication/division, (c) powers.

(a) Add absolute errors, (b) add fractional errors, (c) multiply fractional error by the power.