STM0005 Physics: Lecture Notes

Chapter 12 Formula Sheet

The formulas and symbols given here are the ones that you will be given at the front of your exam paper. If there are formulas that are not included here then these are ones that you will need to learn for the exam.

Acceleration due to gravity \(g=9.8\text {m/s}^{2}\).

Algebraic equations

The quadratic formula:

\begin{equation*} x=\frac {-b\pm \sqrt {b^{2}-4ac}}{2a} \end{equation*}

Geometrical Equations

Arc length \(=r\uptheta \)

Circumference of a circle \(=2\uppi r\)

Area of a circle \(=\uppi r^{2}\)

Curved surface area of a cylinder \(=2\uppi r h\)

Area of a sphere \(=4\uppi r^{2}\)

Volume of a sphere \(=\frac {4}{3}\uppi r^{3}\)

Mechanics Equations

Velocity and acceleration

\begin{equation*} v=\frac {\Delta s}{\Delta t}, \qquad a=\frac {\Delta v}{\Delta t} \end{equation*}

Equations of motion

\begin{align*} v&=u+at, \qquad s=\left (\frac {u+v}{2}\right )t,\\ v^{2}&=u^{2}+2as, \qquad s=ut+\frac {1}{2}at^{2} \end{align*}

Force

\begin{equation*} F=ma, \qquad F=\frac {\Delta \left (mv\right )}{\Delta t} \end{equation*}

Impulse

\begin{equation*} F\Delta t =\Delta \left (mv\right ) \end{equation*}

Work, energy, and power

\begin{align*} W&=Fs\cos \uptheta , \qquad E_{K}=\frac {1}{2}mv^{2},\\ \Delta E_{P}&=mg\Delta h, \qquad P=\frac {\Delta W}{\Delta t},\\ P&=Fv, \qquad \text {Efficiency}=\epsilon =\frac {\text {useful output power}}{\text {input power}} \end{align*}

Circular Motion Equations

Angular velocity

\begin{equation*} \uw =\frac {v}{r}, \qquad \upomega =2\up f \end{equation*}

Centripetal acceleration

\begin{equation*} a=\frac {v^{2}}{r}=\upomega ^{2}r \end{equation*}

Centripetal force

\begin{equation*} F=\frac {mv^{2}}{r}=m\upomega ^{2}r \end{equation*}

Simple Harmonic Motion Equations

Acceleration

\begin{equation*} a=-\upomega ^{2}x \end{equation*}

Displacement

\begin{equation*} x=A\cos \left (\upomega t+\upphi \right ) \end{equation*}

Speed

\begin{equation*} v=\pm \upomega \sqrt {A^{2}-x^{2}} \end{equation*}

Maximum speed

\begin{equation*} v_{\text {max}}=\upomega A \end{equation*}

Maximum acceleration

\begin{equation*} a_{\text {max}}=\upomega ^{2}A \end{equation*}

Hooke’s law

\begin{equation*} F=-kx \end{equation*}

Mass spring system

\begin{equation*} T=2\uppi \sqrt {\frac {m}{k}} \end{equation*}

Simple pendulum

\begin{equation*} T=2\uppi \sqrt {\frac {l}{g}} \end{equation*}

Electrical circuits Equations

Current and potential difference

\begin{equation*} I=\frac {\Delta Q}{\Delta t}, \quad V=\frac {W}{Q}, \quad V=IR \end{equation*}

Resistors in series

\begin{equation*} R_{T}=R_{1}+R_{2}+R_{3}+\dots \end{equation*}

Resistors in parallel

\begin{equation*} \frac {1}{R_{T}}=\frac {1}{R_{1}}+\frac {1}{R_{2}}+\frac {1}{R_{3}}+\dots \end{equation*}

Power

\begin{equation*} P=IV=I^{2}R=\frac {V^{2}}{R} \end{equation*}

Capacitance

\begin{equation*} C=\frac {Q}{V} \end{equation*}

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