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Physics and Mathematics Core Principles

30 study flashcards covering foundational formulas in mechanics, fluid dynamics, electromagnetism, and calculus for biomedical candidates.

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Kinematic equation relating velocities, acceleration, and displacement

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Kinematic equation relating velocities, acceleration, and displacement

v^{2} = u^{2} + 2 a s

Newton's second law of motion in vector form

\sum F = m \cdot a

Work-energy theorem

W_{net} = Δ K = \frac{1}{2} m v_{f}^{2} - \frac{1}{2} m v_{i}^{2}

Hooke's law and elastic potential energy of a spring

F = - k x

and

U_{s} = \frac{1}{2} k x^{2}

Centripetal acceleration equation in circular motion

a_{c} = \frac{v ^{2}}{r} = ω^{2} r

Hydrostatic pressure at depth

h

in a static fluid

P = P_{0} + ρ \cdot g \cdot h

Archimedes' buoyant force (

F_{b}

)

F_{b} = ρ_{fluid} \cdot V_{submerged} \cdot g

Equation of continuity for incompressible fluid flow

A_{1} v_{1} = A_{2} v_{2} = Q

(volumetric flow rate is constant).

Bernoulli's equation for steady incompressible flow

P + \frac{1}{2} ρ v^{2} + ρ g h = constant

Poiseuille's law for laminar flow through a cylindrical vessel

Q = \frac{π \cdot Δ P \cdot r ^{4}}{8 \cdot η \cdot L}

(flow is proportional to the 4th power of radius).

Laplace's law for surface tension in a spherical bubble or alveolus

P = \frac{2 γ}{r}

First law of thermodynamics equation

Δ U = Q - W

(

W

is work done by the system,

Q

is heat added).

Carnot engine maximum theoretical efficiency

η = 1 - \frac{T _{C}}{T _{H}}

(temperatures in Kelvin).

Coulomb's law for electrostatic force between point charges

F = k \cdot \frac{∣ q _{1} q _{2} ∣}{r ^{2}}

(

k \approx 9.0 \times 1 0^{9} N \cdot m^{2} / C^{2}

Ohm's law and electrical power equations

V = I \cdot R

and

P = V \cdot I = I^{2} R = \frac{V ^{2}}{R}

Resistors in series and parallel formulas

Series:

R_{eq} = R_{1} + R_{2} + \dots

; Parallel:

\frac{1}{R _{eq}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \dots

Capacitance of a parallel-plate capacitor

C = κ \cdot \frac{ϵ _{0} A}{d}

and stored energy

U = \frac{1}{2} C V^{2}

Magnetic Lorentz force on a moving charged particle

F = q (v \times B)

, magnitude

F = ∣ q ∣ v B sin θ

Faraday's law of electromagnetic induction

E = - \frac{d Φ _{B}}{d t}

where magnetic flux

Φ_{B} = B \cdot A \cdot cos θ

Snell's law of refraction

n_{1} sin θ_{1} = n_{2} sin θ_{2}

(critical angle

sin θ_{c} = n_{2} / n_{1}

for

n_{1} > n_{2}

Thin lens equation and linear magnification

\frac{1}{f} = \frac{1}{d _{o}} + \frac{1}{d _{i}}

and

m = - \frac{d _{i}}{d _{o}}

Photon energy equation and photoelectric effect

E = h f = \frac{h c}{λ}

and

K_{m a x} = h f - Φ

Derivative of

u / v

(Quotient rule)

(\frac{u}{v})^{'} = \frac{u ^{'} v - u v ^{'}}{v ^{2}}

Chain rule for differentiation

\frac{d}{d x} [f (g (x))] = f^{'} (g (x)) \cdot g^{'} (x)

Derivative of

ln (x)

and

e^{k x}

\frac{d}{d x} [ln x] = \frac{1}{x}

and

\frac{d}{d x} [e^{k x}] = k e^{k x}

Integration by parts formula

\int u d v = uv - \int v d u

Volume of revolution around the x-axis (Disk method)

V = π \int_{a}^{b} [f (x)]^{2} d x

Standard normal distribution Z-score equation

Z = \frac{X - μ}{σ}

Binomial probability distribution formula

P (X = k) = (k n) p^{k} (1 - p)^{n - k}

with mean

μ = n p

and variance

σ^{2} = n p (1 - p)

Acoustic impedance (

Z

) in medical ultrasound

Z = ρ \cdot v

(density

\times

speed of sound in tissue).

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