Physical World - Units and Dimensions

Practice flashcards covering the fundamentals of units, systems of measurement (MKS, CGS, FPS), unit conversions, supplementary units, and dimensional analysis based on the Physical World lecture notes.

What is a Unit?

A defined term for measuring any physical quantity.

What are the seven Basic (Fundamental) physical quantities?

1. Mass, 2. Length, 3. Time, 4. Current, 5. Temperature, 6. Amount of substance ($\text{mole}$), 7. Luminous intensity ($\text{Candela}$).

What is a Derived quantity?

A combination of basic quantities. Examples include speed ($m/s$), area ($m^2$), volume ($m^3$), acceleration ($m/s^2$), force ($Newton$), work/energy ($Joule$), and pressure ($Pascal$).

What is the formula and derived SI unit for Force?

$F = ma$. Unit: $Newton (N) = kg \, m / s^2$.

What is the formula and derived SI unit for Pressure?

$Pressure = \frac{Force}{Area}$. Unit: $Pascal (Pa) = N / m^2 = kg \, m^{-1} \, s^{-2}$.

What is the formula and unit for Resistance ($R$)?

$R = \frac{V}{I}$. Unit: $ohm (\Omega) = kg \, m^2 \, s^{-3} \, A^{-2}$.

What is the formula for Specific heat capacity ($s$)?

$s = \frac{Heat}{m \Delta T}$. Unit: $J \, kg^{-1} \, K^{-1} = m^2 \, s^{-2} \, K^{-1}$.

What is the relationship between Newtons ($N$) and dynes?

$1 \, N = 10^5 \, dyne$.

What is the relationship between Joules ($J$) and ergs?

$1 \, J = 10^7 \, erg$.

What is the value of the Universal Gravitational Constant ($G$) in MKS and CGS units?

MKS: $6.67 \times 10^{-11} \, N \, m^2 \, kg^{-2}$. CGS: $6.67 \times 10^{-8} \, dyne \, cm^2 \, gm^{-2}$.

What is the conversion between the SI unit Tesla and the CGS unit Gauss for a Magnetic field ($B$)?

$1 \, Tesla = 10^4 \, Gauss$.

How many radians are in $360^{\circ}$?

$2\pi \, radian$.

What is the formula for a Solid angle ($\Omega$) and its unit?

$\Omega = \frac{\text{Surface Area}}{(\text{Radius})^2}$. Unit: Steradian ($str$).

What is the dimensional formula for Force?

$[MLT^{-2}]$.

What is the dimensional formula for Work or Energy?

$[ML^2T^{-2}]$.

What is the dimensional formula for Power?

$[ML^2T^{-3}]$.

What is the dimensional formula for the Coefficient of viscosity ($\eta$)?

$[ML^{-1}T^{-1}]$.

What is the dimensional formula for the Stefan Boltzmann Constant ($\sigma$)?

$[MT^{-3}\theta^{-4}]$.

Which two physical quantities share the same dimensional formula as Planck constant ($h$)?

Angular momentum ($mvr$).

What is the dimensional formula for Plane angle and Solid angle?

They are dimensionless: $[M^0L^0T^0]$.

What is the Principle of Homogenity (POH)?

We can compare two quantities only if their dimensional formula is the same. It also follows that we can only add or subtract physical quantities with the same dimensional formula.