Acceleration

In everyday language, acceleration just means getting faster and faster.  In Physics, however, getting faster and faster is just one example of an acceleration but there are plenty of others - including some where an accelerating object moves at the constant speed.

For physicists, the definition of acceleration is very precise - it is the rate of change of velocity.  It is important to know whether one is considering the instantaneous acceleration or the average acceleration.  

As velocity is a vector quantity it is quantified by two things - the number (with units) e.g. 2.50 m s^-1 and a direction e.g. East.  (see additional comments below under “Addition” and the “Vector” entry in the A to Z of concepts).  This means vector mathematics is needed when either the number or the directions (or both) change.  Whatever the situation, it is still correct to say that

Final velocity = Initial velocity +change in velocity

but you have to remember both the numbers and the directions.

In mathematical notation the acceleration is:

a_{}_{\text{instantaneous}}=\frac{dv}{dt}

a_{average}=\frac{\Delta v}{\Delta t}

or in a word equation:

\text{a}_{\text{average}}\text{=}\frac{\text{change in velocity}}{\text{time taken}}

For example, an object stays at the same speed of 2.50 m s^-1 but, in 2.0 seconds, it changes direction from going East to going South.  The acceleration is worked out as follows:

Final velocity = Initial velocity +change in velocity

\text{accelertion = }\frac{\text{change in velocity}}{\text{time taken}}=\text{ }\frac{\text{3.54}}{\text{2.0}}= 1.77 ms^-2

Addition

Addition does not sound like a difficult concept.  Surely everybody knows that 1+2 = 3?  Trouble is, this simple idea is not always enough - the concept of Addition needs refinement.  

Firstly, the units are really important as you can only add together two (or more) things that have the same unit.  1 banana + 2 bananas = 3 bananas but 1 banana + 2 apples can't be added unless you use a different unit (1 piece of fruit + 2 pieces of fruit = 3 pieces of fruit). 

Units are important in all Physics equations.  For example, a constant acceleration equation is s=ut+\tfrac12at^2.  For this addition to work, utmust have the same units as \tfrac12at^2and their units must also be the same as s.

utis in (ms^-1 x s) which is m. \tfrac12at^2is in (ms^-2 x s²) so again this is in m meaning they can be added together.  The result,s , is also in m. 

Secondly sometimes you have to consider direction. There's a whole class of quantities called vectors that have a direction associated with them.  The result of an addition of vectors depends on both the values and the directions involved.  If you add a 3N force to a 4 N force you can get anything between 1N and 7 N depending on the directions. E.g. if they were at right angles to one another, a 3N force added to a 4 N force would give a 5 N force.

Angle

The angle between two directions is a measure of the fraction of a circle that has been turned when you go from the first direction to the second. 

The fraction of the circle completed is the length of the arc divided by the total circle circumference:

\text{fraction of circle completed = }\frac{\text{arc length, s}}{\text{circumferenc, 2}\pi r}

The two most common units to express angle are degrees and radians.

When measuring an angle in degrees, use of this unit defines a full circle to be 360°. 
This is useful as 360 can be easily divided up into lots of small fractions.  360 is divisible by 2, 3, 4, 5 & 6

\text{angle in degrees =}\frac{s}{2\pi r}\text{x 360}

When measuring an angle in radians, use of this unit defines a full circle to be2\pirad.  
This is useful as the2\pifactor cancels out. 

\text{angle in radian =}\frac{s}{r}

 In Physics, most of the time, it is better to use radians than degrees.

Atomic theory

Put simply, Atomic theory suggests that everyday examples of physical matter matter (both living, dead and never alive) are simply a combination of a large number of individual atoms.  These atoms can combine together into larger structures, called molecules.  Molecules can also combine together to create even larger structures. At the time of writing, IUPAC - the International Union of Pure and Applied Chemistry - has recognised and named a total of only 118 different possible atoms.  These form all the different chemical elements of the periodic table. 

The idea that every single macroscopic object in the world is made up of a different combination of a large number of a small number of discrete atoms is certainly not intuitive.  This simple idea, which gives a microscopic view of the structure of the universe, underpins many scientific ideas and principles. Understanding how and why these atoms interact with one another, and what lies within their structure, is the basis of many branches of physics.  The experimental justification that underpins modern atomic theory is a large body of work and a hugely important modern scientific development.   

One of the foremost Physicists of the twentieth centaury, Richard Feynman, went as far as to suggested that Atomic theory is one of the most powerful scientific concepts ever conceived. In The Feynman Lectures on Physics. Vol. 1. by Feynman, R. P.; Leighton, R.B.; Sands, M. (1963) he writes "If, in some cataclysm, all… …scientific knowledge were to be destroyed [except] one sentence… ….what statement would contain the most information in the fewest words? I believe it is… ….that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another ..."    

Next letter: Background radiation, Back emf, Blackbody radiation & Boltzmann's constant.