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Summary Notes for STEM12
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lecture notes for grade 12 STEM
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Voorbeeld van de inhoud
ESTIMATING UNCERTAINTY IN REPEATED MEASUREMENTSUsing a digital instrument, you time the period of oscillation of a pendulum and find T = 0.44 seconds.
This single measurement of the period suggests a precision of ± 0.005 s, but the precision may not give a
complete sense of the uncertainty. If you repeat the measurement several times and examine the
variations among the measured values, you can get a better idea of the uncertainty in the period. For
example, here are the results of 5 measurements, in seconds: 0.46, 0.44, 0.45, 0.44, 0.41.
Another way to express the variations among the measurements is to use the average deviation. This
statistic tells us on average (with 50% confidence) how much the individual measurements vary from the
mean. However, the standard deviation is the most common way to characterize the spread of a data
set. The standard deviation is always slightly greater than the average deviation, and is used because of
its association with the normal distribution that is frequently encountered in statistical analyses.
STANDARD DEVIATION
To calculate the standard deviation for a sample N measurement: 1. Sum all the measurements and
divide by N to get the average, or mean. 2. Now, subtract this average from each of the N
measurements to obtain N “deviations”. 3. Square each of these deviations and add them all up. 4.
Divide this results by (N -1) and take the square root. The significance of the standard deviation is this: if
you now make one more measurement using the same meter stick, you can reasonably expect that the
new measurement will be within 0.12 cm of the estimated average of 31.19 cm.
What are physical quantities and standards?
In physics and in other branches of science, the quantities used to describe nature are defined so that
they have the same meaning for any person using them. Quantities such as time, length, speed, and
pressure can be measured and given specific values. Each quantity, when measured, has magnitude (a
number) and a unit of measure. We can see that it is important to have standards that are precisely
defined and are used in common by people involved in trade, science and industry. The unit of length
presently in science is called meter. It was originally defined as a distance between two lines inscribed
on a bar of metal stored in a special vault in a small town near Paris, France. Replicas made from
standard were distributed around the world. A meter in France had the same length as a meter in
Canada, as used in any other country.
SCALAR AND VECTOR QUANTITIES
Scalar is a quantity with magnitude and usually a unit of measure. Scalars are given algebraic symbols
such as E, t and v. The familiar rules of algebraic addition, subtraction, multiplication, and division are
used to mathematically manipulative scalars. Often, we need to indicate the direction as well as the
magnitude of a quantity. Perhaps you have been told that a hidden treasure has a “displacement” from
you of 100 miles in a direction 50º north of west. Displacement is a vector quantity indicating (1) the
distance from one point to another and (2) the direction of an arrow pointing from the first to the
second point. Distance is the corresponding scalar quantity; it indicates only the separation of the
points, not the direction from one to the other. A vector is a quantity with magnitude, direction, and
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