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# H2 Physics Formula

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Following is a working list of H2 Physics formula and some of the derivations that may not be shown in your JC lecture notes.

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## Kinematics

$v = u + at$
$v^2 = u^2 + 2as$
$s=ut + \frac{1}{2}at^2$

## Measurement

If $A = B \pm C$
$\Delta A = \Delta B + \Delta C$
If $A = BC^k$
$\frac{\Delta A}{A} = \frac{\Delta B}{B} + k\frac{\Delta C}{C}$

## Forces and Dynamics

$F = kx$

For springs in series:
$k_{T} = \frac{1}{k_{1} + k_{2} + … + k_{n}}$

For springs in parallel:
$k_{t} = k_{1}+k_{2}+ … + k_{n}$

$p = \rho gh$
$U = m_{fluid.displaced}g$
$\quad = V_{fluid.displaced}\rho g$

$F = \frac{d(mv)}{dt}$
$\quad = m \frac{dv}{dt} + v \frac{dm}{dt}$

Special cases:
if $\frac{dv}{dt} = 0,$
$\quad F = v \frac{dm}{dt}$

if $\frac{dm}{dt} = 0,$
$\quad F = m\frac{dv}{dt} = ma$

$F = \rho Av^2$

Derivation:
$F = \frac{d(mv)}{dt}$
$\quad = \frac{d(\rho Vv)}{dt}$

if v is constant,
$\quad = v\frac{d(\rho V)}{dt}$
$\quad = v\frac{d(\rho Ax)}{dt}$
$\quad = \rho Av\frac{d(x)}{dt}$
$\quad = \rho Av^2$

## Work, Energy and Power

$PE = mgh$
$KE = \frac{1}{2}mv^2$
$EPE = \frac{1}{2}kx^2$
$P = Fv$

## Circular Motion

$a = \frac{v^2}{r} = r\omega^2$
$F = \frac{mv^2}{r} = mr\omega^2$

## Gravitational Field

$F = G\frac{Mm}{r^2}$
$g = G\frac{M}{r^2}$
$U = -G\frac{Mm}{r}$
$\phi = -G\frac{M}{r}$
$F = -\frac{dU}{dr}$
$g = -\frac{d\phi}{dr}$

## Thermal Physics

$PV = nRT$
$T/K = T/C^\circ + 273.15$
$PV = \frac{1}{3} Nm \langle c \rangle ^2$
$\frac{1}{2} m \langle c \rangle ^2 = \frac{3}{2} kT$

## First Law of Thermodynamics

$\Delta U = Q_{in} + W_{on}$
$W = P \Delta V$

## Oscillations

$a = -\omega^2x$ for both

Derivation:
$x = x_{o}sin(\omega t)$ or $x = x_{o}cos(\omega t)$

Differentiating with respect to time,
$v = v_{o}\omega cos(\omega t)$ or $v= -v_{o}\omega sin(\omega t)$

Differentiating with respect to time again,
$a = -v_{o}\omega ^ 2 sin(\omega t)$ or $a = -v_{o}\omega ^2 cos(\omega t)$
or
$a = -\omega^2x$ for both

$v = \pm \omega \sqrt{x_{o}^2-x^2}$

$KE = \frac{1}{2}m\omega ({x_{o}^2-x^2})$
$TE = \frac{1}{2}m\omega {x_{o}^2}$
$PE = TE – KE = \frac{1}{2}m\omega {x^2}$

## Wave Motion

$v = f \lambda$
$I \propto A^2$
$I \propto cos^2 \theta$

## Superposition

$\Delta x = \frac{\lambda D}{a}$
$sin \theta = \frac{\lambda}{b}$
$\theta \approx \frac{\lambda}{b}$
$dsin\theta = n\lambda$

## Electric Fields

$F = \frac{1}{4\pi \varepsilon_{0}} \frac{Q_{1}Q_{2}}{R^2}$
$E = \frac{1}{4\pi \varepsilon_{0}} \frac{Q}{R^2}$
$U = \frac{1}{4\pi \varepsilon_{0}} \frac{Q_{1}Q_{2}}{R}$
$V = \frac{1}{4\pi \varepsilon_{0}} \frac{Q}{R}$
$E = \frac{V}{D}$

## Current of Electricity

$Q = It$
$V = \frac{W}{Q}$
$V = IR$
$P = VI$ or $P = I^2R$ or $P = \frac{V^2}{R}$
$R = \frac{\rho l}{A}$

## D.C. Circuits

For resistors in series:
$R_{T} = R_{1} + R_{2} + … + R_{n}$

For resistors in parallel:
$R_{t} = \frac{1}{R_{1}+R_{2}+ … + R_{n}}$
Potential divider rule:
$V_{1}= \frac{R_{1}} {R_{1} + R_{2} + … + R_{n}} \times V_{t}$

## Electromagnetism

$B = \frac{\mu_{o} I}{2\pi d}$
$B = \frac{\mu_{o} nI}{2r}$
$B = \mu_{o} nI$
$F = BIl sin \theta$
$F = Bqv sin \theta$

## Electromagnetic Induction

$\Phi = BA cos \theta$
$E = \frac{d\Phi}{dt}$

## Alternating Current

$I_{rms} = \frac{I_{o}}{\sqrt{2}}$
$\frac{N_s}{N_p} = \frac{V_s}{V_p} = \frac{I_p}{I_s}$

## Quantum Physics

$\frac{1}{2}mv_{max}^2 = eV_{s}$
$hf = \Phi + \frac{1}{2}mv_{max}^2$
$\lambda = \frac{h}{\rho}$
$hf = E_{2} – E_{1}$
$\Delta p \Delta x \geq h$

## Nuclear Physics

$E = mc^2$
$t_{\frac{1}{2}} = \frac{ln2}{\lambda}$