Units and Measurements — Week 1, Lecture 1

Practice flashcards covering base and derived SI units, order of magnitude, dimensional analysis, uncertainty, and significant figures from Week 1 notes.

What are the seven base SI units?

meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd).

Which base quantity does the meter measure?

Length.

Give an example of a derived SI quantity and its unit.

Area (m^2), speed (m/s), density (kg/m^3).

What is the definition of order of magnitude?

The power of 10 that best approximates a number, indicating its scale.

How do you determine order of magnitude using log10?

Compute log10(N) and round to the nearest integer.

In N = a × 10^n, when is the order 10^n versus 10^(n+1)?

If a < sqrt(10) ≈ 3.16, the order is 10^n; if a > sqrt(10), the order is 10^(n+1).

What is the average speed formula?

Average speed = total distance ÷ time.

What defines the second in SI units?

The second is defined by 9,192,631,770 vibrations of a cesium-133 atom.

How is the meter defined?

Distance that light travels in 1/299,792,458 of a second.

How is the kilogram defined?

Defined via Planck constant and the Kibble balance.

What does kilo (k) mean in SI prefixes?

10^3.

What does nano (n) mean in SI prefixes?

10^-9.

What does micro (µ) mean in SI prefixes?

10^-6.

How many atoms span the Sun’s diameter, given a hydrogen atom ~1e-10 m and Sun ~1e9 m?

About 10^19 atoms.

What is accuracy in measurement?

How close a measurement is to the true value.

What is precision in measurement?

How close repeated measurements are to each other.

Name common sources of measurement uncertainty.

Limitations of the measuring device, skill of the measurer, irregularities in the object, situational factors.

What is percent uncertainty?

Percent uncertainty = (δA / A) × 100%.

What is dimensional analysis?

A method to check equations for consistent dimensions; trig/log/exp inputs must be dimensionless.

What is the dimension of mass flow rate?

M T^-1.

What is the dimension of volumetric flow rate?

L^3 T^-1.

What is the dimension of ρ dV?

M.

What are dimensionless quantities?

Quantities with no dimensions (exponents are all zero).

What are the rules for significant figures in multiplication and division?

The result has the same number of significant figures as the least precise input.

What are the rules for significant figures in addition and subtraction?

The result has no more decimal places than the least precise measurement.

What is estimation in physics good for?

Back-of-the-envelope calculations to develop intuition, sanity-check designs, and assess feasibility.