Physics and Maths Tutoring

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A level, I/GCSE, & Functional Skills Tutoring
in Physics & Maths

One-to-one tuition on-line from
Michael A Smith
MInstP BSc(Hons) NatSciPhys & Math
son of David M Smith

A tutor with nineteen years of experience & dedication with extensive knowledge of both physics & maths
at A level, IGCSE, GCSE, & Functional Skills Maths

Introductory session: free & without obligation

Bookings now being taken for June 2023 onwards

Contact Michael on
0 75 84 47 60 13
or via mike.smith@physics.org

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Types of Homework

There are seven types of homework. These are practice, preparation, extension, integration, research, application, & flipped homework.
Each type of homework has its own role for students learning. The important task for teachers is to select homework that will best provide holistic support to a student.

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emf & pd

In any circuit there are components that put energy into the circuit, they provide an electro-motive force (emf), & components that take energy out, they have a potential difference (pd) across them. Both emf & pd are measure in volts, $V$.

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12 Female Physicists

Marie Curie

only person to have Nobel Prizes in multiple sciences;

Lise Meitner

the 1^st woman to be appointed Professor of Physics in Germany;

Maria Goeppert Mayer

proposed the nuclear shell model;

Ruby Payne-Scott

discovered several types of radiation bursts originating from the sun;

Rosalind Franklin

her expertise was instrumental in producing the 1^st X-ray diffraction images of DNA, confirming its double helix structure;

Vera Rubin

conducted pioneering work on galaxy rotation rates, providing evidence for the existence of dark matter;

Dame Jocelyn Bell Burnell

co-discovered the 1^st radio pulsars;

Katherine Johnson

her calculations of orbital mechanics made possible the 1^st & subsequent manned U.S. spaceflights;

Helen Quinn

developed the theory, which is related to matter-antimatter symmetry & explains a possible source of dark matter;

Margaret Reid

is carrying out pioneering on fundamental tests of quantum theory, applications include teleportation & cryptography;

Amanda Barnard

she became the 1^st woman & the 1^st person in the Southern Hemisphere to win the Feynman Prize in nanotechnology for her work on diamond nanoparticles;

Michelle Simmons

She has established a large research group dedicated to the fabrication of atomic scale devices, the only group worldwide that can create atomically precise devices in silicon.

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Simple Harmonic Motion

One type of motion that repeats. The more well know circular motion (orbital motion for planets) has links to SHM.

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Rules for Divisibility

Divisible by means when you divide one number by another the result is a whole number. Numbers like 555 are clearly divisible by five, but could you see that 555 is also divisible by three, fifteen, 37, 111, & 185? Methods are given here to identify divisibility by integers up to 12, and beyond if should you wish.

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G and E Fields Compared

Force in a Radial Field
Gravitational Field $$F=\frac{G{m}_1{m}_2}{r^2}$$ Always attractive This is a vector	Electric Field $$F=\frac{k{Q}_1{Q}_2}{r^2}$$ Can be attractive or repulsive This is a vector

The radial field equations isn't the only property that is similar between these fields.

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Quadratic Sequences

A quadratic sequence has $n^2$ & no higher powers of $n$ in its $n^{\mathrm{th}}$ term ($U_n$). The general form of a quadratic sequence is given by $$U_n=a{n}^2+bn+c$$ where $a$, $b$ & $c$ are numbers that can be thought of as characterising the quadratic sequence & often are to be found.

An example of a quadratic sequence is 1, 4, 9, 16, 25, ... which happens to be the square numbers. Another is 3, 6, 13, 24, 39, ... which is less easily identified as a particular sequence. To determine if a given sequence is indeed a quadratic sequence the second difference needs to be shown to be constant.

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Set Notation

A set is a collection of objects, elements or members. The objects can be any collection you can think of. This collection can be described by listing the elements, or by giving a rule. The list or rule is given in a pair of curly brackets {}. For example: $A=\{6,9,14\}$ or $B=\{x:x^2+5|x\in \mathbb{N}\}$

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Physics Equations & Data

Equations are central to understanding physics. Each examination boards issues a list of equations for use in their tests which are either to be memorised or given to the candidate in a booklet.

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SUVAT

The Equations of Constant Acceleration

Let s be the displacement, u be the initial velocity, v be the final velocity, a be the constant acceleration, & t be the time taken, then ...

Further details can be found at Wikipedia: Equations of motion - Uniform acceleration

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Useful Physics Websites

A list of websites grouped according to qualifications that students may find useful in revision & preparation for exams.

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All measurements we make have a level of uncertainty

the Limitation of Physical Measurements

But how do we combine uncertainties?

● Adding / subtracting - ADD ABSOLUTE UNCERTAINTIES
e.g. A ruler with an uncertainty of $0.5\mathrm{mm}$ shows a spring extends from $50.0\mathrm{mm}$ to $63.5\mathrm{mm}$, so the extension is $63.5-50.5=13.5$ with an uncertainty of $0.5+0.5=1$. The calculated extension is $(13.5\pm 1)\mathrm{mm}$

● Multiplying / dividing - ADD RELATIVE UNCERTAINTIES
e.g. a force of $(45\pm 5)\mathrm{N}$ is applied to a mass of $(9\pm 3)\mathrm{kg}$, what is the acceleration? Using Newton's 2^nd Law, the acceleration is given by $a=\frac{F}{m}$, so $a=\frac{45}{9}=5\mathrm{m}{\mathrm{s}}^{-2}$ with a certainty given by $\frac{5}{45}+\frac{3}{9}=\frac{4}{9}$. The calculated acceleration is $5\mathrm{m}{\mathrm{s}}^{-2}\pm \frac{4}{9}$ or $(5\pm 2)\mathrm{m}{\mathrm{s}}^{-2}$

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Recommended Calculators

A list of calculators that are useful for I/GCSE & A Level Maths or physics

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Moments

In physics, a moment is an expression involving the product of a distance & physical quantity, & in this way it accounts for how the physical quantity is located or arranged.
Moments are usually defined with respect to a fixed reference point; they deal with physical quantities located at some distance relative to that reference point. For example, the moment of force, often called torque, is the product of a force on an object & the distance from the reference point to the object. In principle, any physical quantity can be multiplied by a distance to produce a moment. Commonly used quantities include forces, masses, & electric charge distributions. [scraped from en.wikipedia.org/wiki/Moment_(physics)]

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Photoelectric Effect

The Photoelectric effect provides evidence that electromagnetic waves have particle-like behaviour. In the photoelectric effect, electrons are emitted from a metal’s surface when it absorbs electromagnetic radiation.

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Fraction, Decimals & Percents

You're unlikely to be asked to convert between one seventh & the decimal equivalent of 0.1428571428571 ...
These are, however, the same number, but in different presentations.
See more at mathsisfun.com

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Evolution of Large Mass Stars

The evolution of stars with a mass higher than about 1.4M_Sun is different from that of smaller mass stars. Stars between 1.4M_Sun & 3M_Sun also evolve into red giants, but they end their life as supernovae, leaving behind a neutron star. Stars with a main-sequence mass of more than 3MSun evolve into red supergiants, & when these explode as supernovae they leave behind a black hole.

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