1. Measurement 20230624

Measurements Base Quantities and Units Mass Length Time Current Temperature Amount of Substance Luminous Intensity kg m s A K mol cd Homogeneity of Physical Equations • Expressions separated by “+”, “–“ and “=” have the same units Prefixes pico nano micro milli centi deci kilo mega giga terra p n µ m c d k M G T 10-12 10-9 10-6 10-3 10-2 10-1 103 106 109 1012 Uncertainty and Derived Uncertainty Addition and Subtraction Multiplication and Division • c ma nb= (m and n are constants) o c m a n b  =+ , ALSO: o 1na c bmm  =+ *, and o 1mb a cnn  =+ * • xy z ma bc d= (m,x,y and z are constants) o c a b dx y zc a b d    =++ Note: • a, b, c and d are independent from one another. 1. If not, use the maximum and minimum value, max minccc 2 −= • *Make the derived quantity the subject first before applying the rule Half is a numerical constant with no units But not all constants are unitless. g = 9.81 m s-2 is a constant with units kg m s -2 is the SI base unit of force while N is the SI unit.

Errors / Uncertainties Absolute Fractional Percentage c c c  c 100%c   Random Error A random error is an error which gives a scatter of readings about an average value. It has an equal chance of being positive or negative and can be reduced by averaging. Systematic Error A systematic error is a constant deviation of readings from the true value in one direction. All measurements will be too high or too low by the same amount. It can be reduced by correct laboratory practice. Precision (of an instrument): a term used to describe the level of uncertainty in an instrument’s scale. High precision instruments have small scale divisions. Accuracy (of an instrument): is the closeness of a reading on an instrument to the true value of the quantity being measured. An accurate instrument will give readings close to the true values. Precision (of a set of readings): is the degree of closeness of the readings with one another. It is associated with small random error. Accuracy (of a set of readings): is the degree of closeness of the average value of the readings to the true value. It is associated with small systematic error. Vectors • Have directions and magnitudes • Therefore, when we say there is a change in a vector, it could mean 1. Magnitude change only; or 2. Direction change only; or 3. Both magnitude and direction change • “Change” in a quantity means how different is the final quantity from the initial quantity. Therefore in mathematical equation, for example, a change in velocity means final initialv v v =− 1. The equation above is a vector equation. Refer to above bullet points on what does a “change” means. See below on evaluating a change in vector. 2. To evaluate a vector equation, drawing the vectors and use geometry to determine both magnitude and direction of the final vector.

Vectors Manipulation Vector A Vector B C = A + B C = A – B A B B A C - B A C