Formula Recall & Rearrange Drills
Paper 2 is "shove the numbers into the formula booklet" — but only if you can rearrange the equation first. Work through these ten OCR A formulae from Module 5 & 6 — fields, capacitors, magnetic fields, oscillations and nuclear physics, the content Y13 builds on.
Centripetal Force
\[F = \dfrac{mv^2}{r}\]
Variables
F
Centripetal forcem
Massv
Speedr
RadiusPractice
Rearrange $F=\dfrac{mv^2}{r}$ to make $r$ the subject.
A $0.20\ \text{kg}$ ball moves in a circle of radius $0.50\ \text{m}$ at $4.0\ \text{m s}^{-1}$. Find the centripetal force $F$.
SHM Displacement
\[x = A\cos(\omega t)\]
Variables
x
DisplacementA
Amplitudeω
Angular frequencyt
TimePractice
At $t=0$, what does $x=A\cos(\omega t)$ simplify to?
Rearrange $x=A\cos(\omega t)$ to make $\cos(\omega t)$ the subject.
Newton's Law of Gravitation
\[F = \dfrac{Gm_1m_2}{r^2}\]
Variables
F
Gravitational forceG
Gravitational constantm₁, m₂
Massesr
SeparationPractice
Rearrange $F=\dfrac{Gm_1m_2}{r^2}$ to make $r$ the subject.
Rearrange $F=\dfrac{Gm_1m_2}{r^2}$ to make $m_1$ the subject.
Gravitational Field Strength
\[g = \dfrac{GM}{r^2}\]
Variables
g
Gravitational field strengthG
Gravitational constantM
Mass of the bodyr
Distance from centrePractice
Rearrange $g=\dfrac{GM}{r^2}$ to make $r$ the subject.
The Moon has mass $7.35\times10^{22}\ \text{kg}$ and radius $1.74\times10^{6}\ \text{m}$. Taking $G=6.67\times10^{-11}\ \text{N m}^2\text{kg}^{-2}$, find the surface gravitational field strength $g$ of the Moon.
SHM Velocity
\[v = \pm\,\omega\sqrt{A^2 - x^2}\]
Variables
v
Velocityω
Angular frequencyA
Amplitudex
DisplacementPractice
At $x=0$ (the equilibrium position), what does $v=\pm\omega\sqrt{A^2-x^2}$ simplify to?
A mass oscillates with amplitude $A=0.080\ \text{m}$ and angular frequency $\omega=5.0\ \text{rad s}^{-1}$. Find its maximum speed.
Ideal Gas Law
\[pV = nRT\]
Variables
p
PressureV
Volumen
Number of molesR
Molar gas constantT
TemperaturePractice
Rearrange $pV=nRT$ to make $T$ the subject.
$0.50\ \text{mol}$ of an ideal gas occupies $6.0\times10^{-3}\ \text{m}^3$ at a pressure of $2.0\times10^{5}\ \text{Pa}$. Taking $R=8.31\ \text{J mol}^{-1}\text{K}^{-1}$, find its temperature $T$.
Capacitance
\[Q = CV\]
Variables
Q
Charge storedC
CapacitanceV
VoltagePractice
Rearrange $Q=CV$ to make $C$ the subject.
A capacitor stores a charge of $6.0\times10^{-4}\ \text{C}$ when the voltage across it is $12\ \text{V}$. Find its capacitance $C$ in $\mu\text{F}$.
Energy Stored in a Capacitor
\[E = \tfrac{1}{2}QV\]
Variables
E
Energy storedQ
ChargeV
VoltagePractice
Rearrange $E=\tfrac{1}{2}QV$ to make $V$ the subject.
A capacitor stores a charge of $6.0\times10^{-4}\ \text{C}$ at a voltage of $12\ \text{V}$. Find the energy stored $E$.
Force on a Current-Carrying Conductor
\[F = BIL\sin\theta\]
Variables
F
ForceB
Magnetic flux densityI
CurrentL
Lengthθ
AnglePractice
Rearrange $F=BIL\sin\theta$ to make $B$ the subject.
A $0.20\ \text{m}$ length of wire carries a current of $3.0\ \text{A}$ perpendicular to a magnetic field of flux density $0.50\ \text{T}$. Find the force $F$ on the wire.
Activity
\[A = \lambda N\]
Variables
A
Activityλ
Decay constantN
Number of undecayed nucleiPractice
Rearrange $A=\lambda N$ to make $N$ the subject.
A radioactive source has a decay constant $\lambda=2.0\times10^{-3}\ \text{s}^{-1}$ and contains $5.0\times10^{15}$ undecayed nuclei. Find its activity $A$.