Y12 → Y13 Bridge / Formula Drills

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.

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Centripetal Force

$$F = \dfrac{mv^2}{r}$$
Variables F Centripetal force m Mass v Speed r Radius

Practice

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 Displacement A Amplitude ω Angular frequency t Time

Practice

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 force G Gravitational constant m₁, m₂ Masses r Separation

Practice

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 strength G Gravitational constant M Mass of the body r Distance from centre

Practice

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 Velocity ω Angular frequency A Amplitude x Displacement

Practice

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 Pressure V Volume n Number of moles R Molar gas constant T Temperature

Practice

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 stored C Capacitance V Voltage

Practice

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 stored Q Charge V Voltage

Practice

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 Force B Magnetic flux density I Current L Length θ Angle

Practice

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 Activity λ Decay constant N Number of undecayed nuclei

Practice

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 $A$.

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