Working as a Physicist

A-Level Physics topic one

Validity

A measurement is valid if it measures what it is supposed to be measuring

True value

The value that would have been obtained in an ideal measurement

Accuracy

How close a measurement is to its true value. A measurement result is considered accurate if it is judged to be close to the true value.

Precision

A quality denoting the closeness of agreement (consistency) between values obtained by repeated measurement

Repeatability

The precision obtained when measurement results are obtained by a single operator using a single method over a short timescale. An experiment is said to be repeatable if the same person with the same equipment obtains the same result when doing the same experiment a number of times, over a short time period.

Reproducibility

The precision obtained when measurement results are obtained by different operators using different pieces of apparatus. An experiment is said to be reproducible if different people with different equipment, measuring the same quantity, get a similar result. This is a harder test of the quality of data.

Uncertainty

The range of values within which the true value can be considered to lie with a given level of confidence or probability. A quantification of the doubt about the measurement result.

Error

The difference between the measurement result and the true value if a true value is thought to exist. This is not a mistake in the measurement. The error can be due to both systematic and random effects and an error of unknown size is a source of uncertainty.

Resolution

The smallest measuring interval and the source of uncertainty in a single reading.

Significant figures (SF)

The number of SF used in recording the measurements depends on the resolution of the measuring instruments and should usually be the same as given in the instrument with the fewest SF in its reading.

SI base units

Mass-kg
Length-Metres
Time-Seconds
Current-Amps
Temp-Kelvin
Amount of Substance-Moles
Luminous Intensity-Candela

acceleration unit

m/s^2

density

kg/m^3

charge

Amps * seconds

force

kg*acceleration

energy

1/2 mv^2

exact

10^8

peta

10^15

tera

10^12

giga

10^9

mega

10^6

kilo

10^3

deci

10^-1

centi

10^-2

micro

10^-6

nano

10^-9

pico

10^-12

femto

10^-15

atto

10^-18

random error

Measurements vary due to unpredictable circumstances. They cannot be corrected and
can only be mitigated by making more measurements and calculating a new mean.

Systematic error

Measurements differ from the true value by a consistent amount each time. They can be corrected by using a different technique to take measurements and calibrating measuring instruments.

Precision vs Accuracy

Difference between Accuracy and Precision

Accurate data need to very close to the target value, but precise data need not be close to the target value. Precise data only need to be close together.

For quality purposes, accuracy is desired while precision is not. Precision is required when it is coupled with accuracy.

Accurate data can be precise but precise data may or may not be accurate. Precision is not dependent on accuracy.

For accuracy, one measurement is enough; however, for precision many measurements are required.

Absolute Uncertainty

± smallest significant figure

Percentage uncertainty

fractional uncertainty *100

Single readings

The uncertainty is simply a result of half the resolution of the measuring device

Repeated Readings

For a simple analysis we may consider the uncertainty to be half of the range in the results.

Combining uncertainties

is a value is put in the equation you add its uncertainty to the total uncertainty

reading vs measurements

reading= half resolution, no zero error
measurement=resolution, zero error so double

Displacement (distance)/time graphs

x axis=time, y axis=distance
gradient= velocity of object

area under graph= nothing meaningful

Displacement

distance traveled in a particular direction, vector version of distance

Velocity

vector version of speed

velocity=

speed/time

acceleration=

(final velocity-initial velocity)/time

velocity/time graphs

time=x axis, velocity=y axis
gradient=acceleration of object

area under line= displacment

curved line on acceleration/time graph shows= changing acceleration= jerk (they will legit never ask you this on an exam)

acceleration going past the x axis means a change in direction

Acceleration/time graphs

gradient=jerk
area under line/curve=velocity