Units and Measurements

Practice flashcards covering units of measurement, significant figures, rounding rules, errors, and dimensional analysis from basic physics lecture notes.

Parallax Method

A method used to measure large distances.

$1^\circ$ (Degree)

$$1.745 \times 10^{-2}\,\text{rad}$$

$1'$ (Arc minute)

$$2.91 \times 10^{-4}\,\text{rad}$$

$1''$ (Arc second)

$$4.85 \times 10^{-6}\,\text{rad}$$

Astronomical Unit (AU)

$$1.496 \times 10^{11}\,m$$

Light Year (ly)

$$9.46 \times 10^{15}\,m$$

Parsec

$$3.08 \times 10^{16}\,m$$

Size of proton

$$10^{-15}\,m$$

Radius of Earth

$$10^7\,m$$

Distance to Boundary of Observable Universe

$$10^{26}\,m$$

Radian (rad)

The supplementary SI unit for Plane angle.

Steradian (sr)

The supplementary SI unit for Solid angle.

Kelvin (K)

The SI base unit for Temperature.

Candela (cd)

The SI base unit for Luminous intensity.

Mole (mol)

The SI base unit for Amount of substance.

Caesium clock

The basis for the SI unit of time (second) with an uncertainty less than 1 part in $10^{-13}$ (equivalent to $3\,\mu s$ loss every year).

Unified atomic mass unit (amu)

$(1/12)^{th}$ mass of one $C12$ atom, equal to $1.66 \times 10^{-27}\,kg$; used to measure mass of atoms and molecules.

Significant Figures

The digits in a measured quantity which are reliable and confidence in our measurement plus the digit which is uncertain.

Significant Figure Rule 1 (Non-zero)

All non-zero digits are significant (e.g., 42.3 has three significant figures).

Significant Figure Rule 2 (Zeros between digits)

A zero becomes significant if it appears between two non-zero digits (e.g., 5.03 has three significant figures).

Significant Figure Rule 3 (Leading zeros)

Leading zeros or the zeros placed to the left of the number are never significant (e.g., 0.045 has two significant figures).

Significant Figure Rule 4 (Trailing zeros)

Trailing zeros or the zeros placed to the right of the number are significant (e.g., 4.330 has four significant figures).

Rounding Rule (Odd-Five)

If the digit to be dropped is 5 or 5 followed by zeros, and the preceding digit is odd, it is raised by one (e.g., 3.750 becomes 3.8).

Rounding Rule (Even-Five)

If the digit to be dropped is 5 or 5 followed by zeros, and the preceding digit is even, it is left unchanged (e.g., 3.250 becomes 3.2).

Systematic Errors

Errors which tend to occur only in one direction, either positive or negative, including Instrumental, Experimental, and Personal errors.

Least count error

The smallest value that can be measured by an instrument; occurs with both random and systematic errors.

Absolute Error ($\Delta a$)

The difference between the true value and the measured value of a quantity: $\Delta a = a_i - a_{mean}$.

Pressure / Stress / Young's modulus

Dimensional formula: $M L^{-1} T^{-2}$

Work / Energy / Torque

Dimensional formula: $M L^2 T^{-2}$

Gravitational constant ($G$)

Dimensional formula: $M^{-1} L^3 T^{-2}$

Permittivity of free space ($\varepsilon_0$)

Dimensional formula: $M^{-1} L^{-3} T^4 A^2$

Dimensionless Quantities

Physical quantities with no dimensions, such as Strain, Refractive index, Relative density, Plane angle, and Solid angle.

Least Count (Vernier Calipers)

$1 MSD - 1VSD$ or $\frac{1}{n} MSD$ if $n$ VSD coincides with $(n-1)$ MSD.

Pitch (Screw Gauge)

The distance moved by the screw per rotation, calculated as $\frac{\text{Main Scale Reading}}{\text{No. of rotations}}$.

Least Count (Screw Gauge)

Formula: $\frac{\text{pitch}}{\text{Total no. of divisions on circular scale}}$