SPH3U The SPH3U Formula Sheet, Decoded: Notes and Practice

You are handed this sheet in every test and on the exam. Having it is not the same as being able to use it — the sheet gives you the equations and tells you nothing about what the symbols mean, which units they need, or when each one applies. This page fills in the missing half.

Fig 1Which strand each block of the sheet belongs to, and where each one is taught.

Read the sheet before the exam, not during it

The sheet is a memory aid, not a substitute for knowing the material. Students who meet it cold lose time hunting for the right line. Spend twenty minutes with this page the night before and you will know where everything sits.

Kinematics

Formula	Finds	Symbols and units	Watch out for
$Δ v = v_{f} - v_{i}$	Change in velocity	$v$ in m/s	Always final minus initial
$Δ d = d_{f} - d_{i}$	Displacement	$d$ in m	Displacement, not distance — direction required
$Δ t = t_{f} - t_{i}$	Time interval	$t$ in s	Convert minutes and hours first
$v = \frac{Δ d}{Δ t}$	Average velocity	m/s	With distance instead, it gives average speed
$a = \frac{Δ v}{Δ t}$	Acceleration	$m/s^{2}$	Sign shows direction, not speeding up or slowing down
$v_{f} = v_{i} + a Δ t$	Final velocity	m/s	The equation missing displacement
$Δ d = v_{i} Δ t + \frac{1}{2} a Δ t^{2}$	Displacement	m	Missing final velocity. Square $Δ t$ first
$Δ d = v_{f} Δ t - \frac{1}{2} a Δ t^{2}$	Displacement	m	Missing initial velocity. Note the minus sign
$v_{f}^{2} = v_{i}^{2} + 2 a Δ d$	Final velocity	m/s	Missing time. Remember the square root at the end

All four kinematic equations require uniform acceleration. Taught in Kinematics.

Forces

Formula	Finds	Symbols and units	Watch out for
$F_{g} = m g$	Weight	$m$ in kg, $F$ in N	Mass in kilograms, never grams
$g = 9.81 m/s^{2} = 9.81 N/kg$	Gravitational constant	Two equivalent forms	Use 9.81, not 9.8 and not 10
$Σ F = F_{n e t} = F_{+} + F_{-}$	Net force	N	Declare a positive direction before adding
$F_{n e t} = m a$	Acceleration or net force	N, kg, $m/s^{2}$	It takes the net force, not any single force
$μ = \frac{F _{f r i c t i o n}}{F _{n or ma l}}$	Coefficient of friction	Unitless	A ratio, so no units. On level ground $F_{N} = m g$

Taught in Forces.

Energy

Formula	Finds	Symbols and units	Watch out for
$W = F \cdot d = F d cos θ$	Work	J	$θ$ is between force and displacement. Degrees mode
$Σ W = W_{n e t} = W_{+} + W_{-}$	Net work	J	Friction contributes negative work
$K E = \frac{1}{2} m v^{2}$	Kinetic energy	J, kg, m/s	Square $v$ first. Never negative
$PE = m g h$	Gravitational PE	J	$h$ is vertical height above a stated reference
$Q = m c Δ T$	Heat for a temperature change	J, kg, $\text{J/{(kg}\cdot^\circ\text{C)}}$	$c$ differs for ice, water and steam
$Q_{re l e a se d} + Q_{ab sor b e d} = 0$	Final temperature of a mixture	J	Write both $Δ T$ as final minus initial
$Q = m L_{f}$	Heat to melt or freeze	J, kg, J/kg	No $Δ T$ — the temperature does not change
$Q = m L_{v}$	Heat to boil or condense	J, kg, J/kg	$L_{v}$ is about seven times $L_{f}$ for water
$A = A_{0} (\frac{1}{2})^{t / h}$	Amount remaining after decay	Any consistent unit	$t$ and $h$ in the same time unit

Taught in Energy and Society.

Waves and Sound

Formula	Finds	Symbols and units	Watch out for
$f = \frac{# cycles}{time} = \frac{1}{T}$	Frequency	Hz, s	Frequency and period are reciprocals
$v = f λ$	Wave speed	m/s, Hz, m	Applies to every wave. The medium sets $v$
$v_{so u n d} = (332 + 0.6 T)$ m/s	Speed of sound in air	$T$ in $^{\circ} C$	Celsius, not kelvin. Air only
$mach # = \frac{v _{o bj ec t}}{v _{so u n d}}$	Mach number	Unitless	Compare with the local speed of sound
$t_{ec h o} = \frac{2 d}{v}$	Echo time or distance	s, m, m/s	The factor of 2 — it is a round trip
$f_{b e a t} = ∣ f_{1} - f_{2} ∣ = \frac{# beats}{time}$	Beat frequency	Hz	Absolute value hides which note is higher
$\frac{I _{2}}{I _{1}} = \frac{r _{1}^{2}}{r _{2}^{2}}$ , $I \propto \frac{1}{d ^{2}}$	Intensity at a new distance	$W/m^{2}$ , m	The radii swap sides. Further away must mean quieter
$d B = 10 lo g (\frac{I _{2}}{I _{1}})$	Decibel difference	dB	$+ 10 dB$ is ten times the intensity
$l_{n} = \frac{nλ}{2}$ , $f_{n} = n f_{0}$	Strings and open pipes	m, Hz	All harmonics present
$l_{n} = \frac{( 2 n - 1 ) λ}{4}$ , $f_{n} = (2 n - 1) f_{0}$	Closed pipes	m, Hz	Odd harmonics only

Taught in Waves and Sound.

Electricity and Magnetism

Formula	Finds	Symbols and units	Watch out for
$I = \frac{q}{Δ t}$	Current	A, C, s	Time in seconds
$R = \frac{V}{I}$	Resistance	$Ω$ , V, A	Rearranges to $V = I R$ and $I = V / R$
$P = V I$	Electrical power	W, V, A	Also $P = I^{2} R$ for line losses
$R_{T, ser i es} = R_{1} + R_{2} + \dots$	Total series resistance	$Ω$	Total exceeds any single resistor
$\frac{1}{R} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \dots$	Total parallel resistance	$Ω$	Take the reciprocal at the end
$F_{M} \propto I$ , $F_{M} \propto n$ , $F_{M} \propto κ$	Electromagnet strength	Proportional only	Qualitative — no numerical field strengths
$\frac{N _{1}}{N _{2}} = \frac{V _{1}}{V _{2}} = \frac{I _{2}}{I _{1}}$	Transformer ratios	Turns, V, A	The current ratio is inverted

Taught in Electricity and Magnetism.

Quantities the sheet uses but never defines

Symbol	Name	Typical value or note
$c$	Specific heat capacity	Water 4180, ice 2100, steam 2010, aluminium 900, iron 450 $\text{J/{(kg}\cdot^\circ\text{C)}}$
$L_{f}$	Latent heat of fusion	Water: $3.34 \times 1 0^{5} J/kg$
$L_{v}$	Latent heat of vaporization	Water: $2.26 \times 1 0^{6} J/kg$
$h$	Half-life	A time, specific to each isotope
$κ$	Core material factor	Soft iron can be in the hundreds
$n$	Turns, or harmonic number	Meaning depends on the equation it appears in
$T$	Period, or temperature	Seconds in wave equations, $^{\circ} C$ in thermal ones

Two symbols that mean different things on the same sheet

T

is a period in the wave section and a temperature in the thermal and sound-speed sections.

n

is a harmonic number in the standing-wave equations and a number of turns for electromagnets. Read them from the context of the equation they appear in, not from the letter alone.

Required formulas that are NOT on the sheet

Memorize these four

The sheet is incomplete, and these four are examinable. Power:

P = \frac{W}{Δ t}

. Efficiency:

\frac{E _{u se f u l}}{E _{t o t a l}} \times 100%

. Average-velocity kinematics:

Δ d = (\frac{v _{i} + v _{f}}{2}) Δ t

, the one missing acceleration. Total mechanical energy:

E_{t o t a l} = K E + PE

, and its conserved form

K E_{i} + P E_{i} = K E_{f} + P E_{f}

Unit conversions — km/h to m/s is a division by $3.6$ ; minutes and hours to seconds; grams to kilograms.
Right-angled vector addition — $R = A^{2} + B^{2}$ and $θ = tan^{- 1} (\frac{opp}{adj})$ , from MCR3U rather than the physics sheet.
Energy cost — $E (kWh) = \frac{P (W) \times t (h)}{1000}$ , and $1 kWh = 3.6 \times 1 0^{6} J$ .
Percent error — $\frac{∣ measured - accepted ∣}{accepted} \times 100%,$ needed in every lab report.

Unit traps worth a final read

g

appears as both

9.81 m/s^{2}

and

9.81 N/kg

— same number, different reading.

T

must be in Celsius for the speed of sound.

t

and

h

must share a unit in the half-life equation. Mass is in kilograms everywhere. And

μ

, Mach number and efficiency ratios are all unitless.

The SPH3U Formula Sheet, Decoded