1. Nota Fizik: Understanding Derived and Base Quantities
Understanding Derived and Base Quantities
Physical quantities are quantities that can be measured. e.g. Length, Temperature,
Speed, Time.
Quantities or qualities that cannot be measured are not physical quantities. e.g.
happiness, sadness etc.
Physical quantities can be divided into Base quantitied and Derived quantities.
(i) Physical quantities are quantities that can be measured or can be calculated.
(ii) The base quantities are “building block” quantities from which other quantities are
derived from.
(iii) The base quantities and their S.I. units are:
 Base quantities S.I. units
 Mass kg
 Length m
 Time s
 Electric current A
 Thermodynamic
 temperature K
(iii) Derived quantities are quantities derived (iv) Examples of derived quantities.
 Derived quantities S.I. units
 area m2
 density kg m-3
 weight N
 velocity m s-1
Standard Notation: To express very large or very small numbers.
Example; A X 10 n (ten to the power of n), n must be an integer and 1 ≤ A <10

2. Nota Fizik: Understanding Scalar and Vector Quantities
Scalar quantities: Quantities that have magnitude only. ( Speed, mass, distance)
Example:
For example speed has unit of ms^-1. but it has no direction.
Mass is kg but we don't know the direction.
Distance is 2km but no direction.
Vector quantities: Quantities that have magnitude and direction. (Velocity, Weight,
Displacement)
Example:
Velocity unit is ms^-1 but we must state the direction that is whether from right to
left.
Weight unit is Kg but the direction is towards the gravity pull of the earth.
Displacement is 2km but to the north from the point of reference.
Posted by O'Deen at 8:47 AM

3. Experimental Errors
When doing experiments there are several errors that we need to consider. For
example the error when taking reading from instruments and also the influence from
the outer surroundings. This is true for all scientific investigations. Even machines
have errors! and they do need to be calibrated consistently!
Error is the difference between the measured value and the real or actual value. (The
difference in reading is known as the error)
Two main types of error are systematic error and random error.
Systematic error occurs when there is an error when reading the scale that is being
used. It is caused by the surroundings, the instrument itself (scale may not be uniform
or even blurred due to wear and tear) and of course the observer error.
Systematic error results in the measurement or reading being consistently over the
actual value OR consistently smaller than the actual value.
There are several possible causes of systematic error:
One of the most common error is the Zero Error. Zero Error is caused if the reading
shown is Not zero when the true value is actually zero. This is most probably caused by
a flaw in the instrument for example when using a ruler that has lost its zero scale due
to wear and tear hence causing an error in the measurement of length.
Wrong assumptions may also cause error, for example if you assume that water boils
at 100 degree celcius but actually its boiling point is higher if there are impurities in
it. (Pure water boils at 100 degree celcius)
There is also a possibility to create error when there is a lag of reaction time. For
example in a sports day, when measuring a 100 m running time using a stopwatch. The
observer may not press the stop button exactly when the foot of the runner touches
the finishing line.
Sometimes, as I have mentioned, instruments that are not properly calibrated could
also cause error and this has to be put in consideration when writing a report or when
there is an anomaly in reading.
Another type of error that needs to be considered is Random Error.
Random error is caused by the observer who reads the measuring instrument. Just like
the systematic error, there can exist positive or negative error. Positive error is when
the reading is bigger than the real value and negative error is when the reading is
smaller than the real value.
One of the ways to reduce random error is to take several readings for a measurement
and then taking the average reading to be analysed.
There are several examples of random error.
Miscounting numbers during observation or change in the surrounding due to

4. temperature, wind, light, exposure to chemicals or impurities may cause error.
Sometimes the observer may read the scale wrongly (as in the case of reading a scale
in on a beaker or ruler (parallax error). Parallax error occurs when a reading is taken
from an unsuitable position relative to the scale.
Ways to reduce error
Magnifying glass to enhance the visual of scale on the instrument.
Avoiding parallax error by positioning the instrument (meter rule) properly on the
table with the eyes perpendicular to the scale. This also applies when reading other
instruments. Parallax error can also be reduced by putting a strip of mirror next to the
scale (for example in ammeter), the eye must be positioned so that the image formed
on the mirror is fully covered by the indicator hand of the ammeter.
Some instruments can be adjusted to eliminate zero error. For example when using an
ammeter, there is an adjuster to set the indicator to zero before making any
measurement.
In the case of a ruler, measurement can be carried out starting from the next clear
scale for example if scale 0.0cm is blurred, we can start measuring the length from
2.0cm, of course taking the difference of value in consideration when recording the
final reading.

5. Nota Fizik: Understanding Measurements
In Physics and any scientific investigations. Measurement of quantities is very crucial.
It is in fact the core of data generation. Measurements can be done by various
methods and various instruments. Here, only a few examples are explained.
A micro balance is used to measure minute masses. It is sensitive but not very
accurate.
Slide callipers are usually used to measure the internal or external diameter of an
object.
A micrometre screw gauge is used to measure the diameter of a wire of the thickness
of a thin object.
All measurement must consider this:
Accuracy: Ability of the instrument to measure the true value or close to the true
value. The smaller the percentage error, the more accurate the instrument is.
Sensitivity of an instrument is the ability of the instrument to detect any small change
in a measurement.
Consistency: ability of the instrument to produce consistent measurement.(the values
are near to each other). The lower the relative deviation, the more consistent the
measurement is.
Ways to increase accuracy:
- repeat the measurements and get the mean value.
- correcting for zero error.
- avoiding parallax error.

6. - use magnifying glass to aid in reading.
For example, when asked about how to increase the sensitivity of a mercury
thermometer:
-use a bulb with thinner wall.
-use a capillary tube of smaller diameter or bore.
Nota Fizik: Analysing scientific investigation
So you are here probably because you want to get a deeper meaning an concept of
scientific investigation.
You should have probably been familiar with the steps involved in scientific
investigation i.e. Identifying problem, making hypothesis, generating data etc...
However, what I would like to emphasis in this post is the different types of variable.
You should know that "A variable is a quantity that varies in value". It represents
"something" that are involved in a measurement in scientific investigation. Thus, a
proper scientific investigation always involve variables and its measurement. A
quantity that can be measured is called a physical quantity.
Three types of variables are:
Manipulated variable is a variable that is set or fixed before and experiment is carried
out. it is usually plotted on x- axis.
Responding variable is a variable that changes according to and dependent to
manipulated variable. it is usually plotted on y-axis.
Fixed variable is fixed and unchanged throughout the experiment.
Now lets see how to make inference and hypothesis?
How to make inference and hypothesis?
Inference: state the relationship between two VISIBLE QUANTITIES in a diagram or
picture.
Hypothesis: state the relation ship between two MEASURABLE VARIABLES that can be
investigated in a lab.
How to tabulate data?
-the name or the symbols of the variables must be labelled with respective units.
-all measurements must be consistent with the sensitivity of the instruments used.
-all the calculated values must be correct.

7. -all the values must be consistent to the same number of decimal places.
A graph is considered well-plotted if it contains the following:
- a title to show the two variables and investigation.
- two axes labelled with correct variables and units
- scales must be chosen carefully and graph must occupy more than 50% of the graph
paper.
- all the points are correctly drawn.
- the best line is drawn.

8. Linear Motion Calculation Examples
A bicycle moved from point A and then moved 50 m to the north in 60 seconds. The
bicycle then moved 120 m to the east in 40 seconds. Finally, it stopped. Calculate the
1. Total distance moved by the bicycle
2. Displacement
3. Velocity
4. Average speed
5. Speed of the bicycle when it is moving to the north
Solution:
1. Total distance = 50m + 170m
= 170m
2. Displacement
Remember displacement is the shortest distance between two points.
Imagine A as the beginning of a triangle. Then connect it with a line of 50m upwards
then it turns left 120m (go east). so the distance is the hypotenuse.
Using Pythagoras' theorem = Squared root (120^2 + 50^2)
= 130m
3. Velocity = Displacement / time
= 130 m / 100 s
= 1.3 m s^-1
4. Average speed of the bicycle = total distance / total time
= 170m/ 100s
= 1.7 m s^-1
5. Speed = distance / time
Distance = 50m, time = 60s
= 50m / 60s
= 0.83 ms^-1
Be careful during calculation as most of the time Physics requires a good skill in
maths!!

9. Distance, Displacement, Velocity, Speed and Acceleration
Distance and Displacement
Distance is the total path length traveled from one location to another. It is a scalar
quantity.
Displacement is the distance between two locations measured along the shortest path
connecting them, in specified location. It is a vector quantity. The SI unit of distance
and displacement is metre (m).
Speed and Velocity
Speed is the distance traveled per unit time or the rate of change of distance.
Speed = total distance traveled / time taken
Velocity is the speed in a given direction or the rate of change of displacement.
Average velocity = displacement/ time taken
Acceleration and Deceleration
Acceleration is the rate of change of velocity.
Acceleration = change of velocity / time taken
Change of velocity = final velocity (v) – initial velocity (u)
Acceleration = (final velocity – initial velocity) / time taken
= (v – u) / t
Things to remember:
1. Constant velocity means the object is not accelerating. Acceleration is zero.
2. Constant acceleration means the object is increasing its velocity.
Label of the Parts

10. (This image is licienced
under GDFL. The source file can be obtained from wikipedia.org)
Range and Accuracy
The range of a micrometer is 0-25mm.
The accuracy of a micrometer is up to 0.01mm.
How to Use a Micrometer?
1. Turn the thimble until the object is gripped gently between the anvil and
spindle.
2. Turn the ratchet knob until a "click" sound is heard. This is to prevent exerting
too much pressure on the object measured.
3. Take the reading.

11. Derived Quantities
A derived quantity is a Physics quantity that is not a base quantity. It is the quantities
which derived from the base quantities through multiplying and/or dividing
them.Example
(Speed is derived from
dividing distance by time.)
Derived Unit
The derived unit is a combination of base units through multiplying and/or dividing
them.
Example 1
Find the derived unit of density.
Answer

12. Unit Conversion
Area and Volume
Example 2
Convert the unit of length, area and volume below to the units given.
a) 7.2 m = ____________cm
b) 0.32 m2 = ____________cm2c) 0.0012 m3 = ____________cm3d) 5.6 cm =
____________m
e) 350 cm2 = ____________m2f) 45000 cm3 = ____________m3Answer
a) 7.2 m = 7.2 x 102 cm
b) 0.32 m2 = 0.32 x 104 cm2 = 3.2 x 103 cm2
c) 0.0012 m3 = 0.0012 x 106 cm3 = 1.2 x 103 cm3
d) 5.6 cm = 5.6 x 10-2 m
e) 350 cm2 = 350 x 10-4 m2 = 3.5 x 10-2 m2
f) 45000 cm3 = 45000 x 10-6 m3 = 4.5 x 10-2 m3

13. Speed
Example 3
Complete the following unit conversion
a) 12 kmh-1 = __________ ms-1
b) 12 ms-1 = __________ kmh-1
Answer
a)
12kmh−1=12km1h=12000m60×60s=3.33ms−1
b)
12ms−1=12m1s=121000km13600h=43.2kmh−1