AQA A-Level Physics Topic 1 - Measurements and Their Errors; made directly in accordance with the AQA 7408 specification
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mass (m)
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kilograms (kg)
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length (l)
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metres (m)
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time (t)
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seconds (s)
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amount of substance (n)
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moles (mol)
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temperature (t)
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kelvin (K)
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electric current (I)
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amperes (A)
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A derived unit is comprised of a combination of SI units.
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These can be derived by using the definition of the unit, or their equations eg. F=ma
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eg. to find the SI units of force (F), multiply the units of mass and acceleration to give kgms^-2 (or N)
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This means that every unit can be broken down into its SI base units.
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Tera (T)
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10^12
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Giga (G)
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10^9
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Mega (M)
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10^6
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Kilo (K)
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10^3
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Centi (c)
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10^-2
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Milli (m)
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10^-3
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Micro (µ)
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10^-6
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Nano (n)
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10^-9
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Pico (p)
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10^-12
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Femto (f)
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10^-15
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It is possible to convert between different units of the same quantity. Here are some examples listed below:
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1 eV = 1.6 × 10^–19 J
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1 kW h = 3 600 000 J or 3.6 MJ (×10^6)
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Random error
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Cause variations in both directions and are usually uncontrollable
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Systematic error
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Caused by faults in the experimental method or apparatus
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Zero error
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A type of systematic error caused by uncalibrated equipment
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Parallax error
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A type of systematic error caused by the apparent position of an object due to the viewing angle
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Precise
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Consistent and fluctuate around a mean value
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Accuracy
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A measurement that is close to the true value
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Repeatability
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The original person can redo the experiement and get the same results
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Reproducibility
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A different person does an experiment differently and gets the same results
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Resolution
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The smallest change in the quantity being measured that gives a recognisable change in reading
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The bounds in which the accurate value can be expected to lie
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They should be given to the same number of significant figures as the data.
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Absolute
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Uncertainty given as a fixed quantity
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Fractional
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Uncertainty as a fraction of the measurement
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Percentage
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Uncertainty as a percentage of the measurement
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Readings are when one value is found
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Measurements are when the difference between 2 readings is found
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The uncertainty in a reading is +/- half the smallest division
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The uncertainty in a measurement is at least +/- 1 smallest division
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The resolution of an instrument will affect its uncertainty
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Digital readings and given values will either have the uncertainty quoted, or assumed to be +/- the last significant digit
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For repeated data, the uncertainty is half the range
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You can reduce uncertainty in the following ways:
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• fixing one end of a ruler so there is only uncertainty in on reading
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• measuring multiple times
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• (for fractional and percentage) measure larger quantities
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Adding/subtracting data - ADD ABSOLUTE UNCERTAINTIES
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Multiplying/diving data - ADD PERCENTAGE UNCERTAINTIES
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Raising to a power - MULTIPLY PERCENTAGE UNCERTAINITY BY POWER
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Uncertainties are shown as error bars on graphs
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A line fo best fit on a graph should go through all error bars (excluding anomalies)
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The uncertainity in a gradient can be found by lines of best and worst fit
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This can be done using the gradients of the steepest and shallowest lines of best fits
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You can also use these two lines to find the uncertainty in the y-intercept
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Orders of magnitude are powers of ten which describe the size of an object
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These can be used to compare the sizes of objects
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Estimation is a skill used to approximate the values of physical quantities, in order to make comparisons, or to check if a value calculated is reasonable.
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Dependant
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The variable that is being measured
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Independent
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The variable that is being changed
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Control
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Other variables that stay the same
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