explain every inmportant point in lecture 01. cover all main point and equation and
example and questions
​
This lecture, the first in a series about measurements and uncertainties in AS Physics
9702, focuses on establishing the fundamental importance of considering uncertainty in any
measurement. Sir Faizan Pasha emphasises that a measurement without considering its
uncertainty is meaningless.
Reading: A reading is simply a single determination of a value by using any apparatus.
The speaker provides examples such as measuring the length of a remote control with a
meter rule, timing an event with a stopwatch, or using a multimeter to find current or voltage.
He stresses that taking a reading is something anyone can do and does not require
specific physics knowledge. It's analogous to using a mobile phone – you learn to use it
without needing a degree.​
●​ Measurement: In contrast, a measurement comes from a series of readings. It
involves giving due respect to the apparatus used, considering its least count, and
taking into account the experimental circumstances and physical constraints. A
true measurement is one where you not only provide the value but also state its
uncertainty. A measurement is only valid when its uncertainty is described.
Without this, the measurement is considered useless. Measurement and uncertainty
go hand in hand.​
The lecture then delves into the concept that every measurement is uncertain to some
extent. There is no such thing as a 100% certain measurement. To illustrate this, the
speaker provides several examples:
●​ Measuring the thickness of a remote:​
○​ Using a meter rule, a reading of 1.7 cm is obtained. However, due to the least
count of the meter rule (0.1 cm, meaning divisions are 1.1, 1.2, 1.3, etc.), one
cannot be certain if the actual thickness is 1.71 cm, 1.72 cm, or another value
close to 1.7 cm.
○​ Using a Vernier calliper, a reading of 1.72 cm might be obtained. While more
precise (it can measure down to 0.01 cm), there is still uncertainty at the next
decimal place (e.g., it could be 1.721 cm, 1.722 cm).
○​ A micrometer screw gauge, even more precise (measuring down to 0.001
cm), might give a reading of 1.724 cm. Yet again, uncertainty exists beyond
this decimal place.
○​ This series of examples demonstrates that as you use more precise
instruments, you can reduce the uncertainty but never eliminate it
entirely. Even with highly sophisticated equipment in places like PCSIR,
where measurements go up to eight or nine decimal places, the subsequent
decimal place remains uncertain.
●​ Measuring the rebound height of a ball:​
○​ Dropping a ball from a certain height (e.g., 40 cm) and trying to measure its
rebound height is presented as an experiment. The speaker notes that it's
difficult to get a precise reading due to factors like the speed of the ball, the
short time it's at its peak, parallax error, and the observer's reaction time.
Even if multiple readings are taken (e.g., around 32 cm), the uncertainty will
be significantly larger than the least count of the measuring scale (which
might be 0.1 cm).
○​ This example highlights that uncertainty is not solely dependent on the
measuring device but also on the experimental conditions and the
observer's limitations (physical constraints). A common mistake students
make is to only consider the instrument's least count when determining
uncertainty, which can lead to incorrect answers in exams.
●​ Estimating the speed of a car:​
○​ When driving at a high speed (e.g., 120 km/h), it's impractical and dangerous
to try and read the speedometer with extreme precision. Even if the
speedometer displays values like 122.5 km/h, the driver's focus is on the
road, and they would likely give an estimate with a larger uncertainty (e.g.,
120 km/h ± 5 km/h) due to the physical constraints of the situation.
The lecture then moves towards a more formal description of uncertainty. Using an example
measurement of X = 42.3 ± 0.1 cm, the speaker explains that the ± 0.1 cm represents the
maximum uncertainty in the measurement. This means the actual value is likely to be
within the range of 42.2 cm to 42.4 cm.
The formal definition provided states: "The uncertainty in a measurement is the interval of
confidence around the measured value such that the measured value is certain not to lie
outside this stated interval". The speaker simplifies this by saying that stating the
uncertainty indicates your confidence that any reasonable repeated measurement by
others under similar conditions will fall within that range. Therefore, by giving an uncertainty,
you are essentially saying, "I am confident that the true value is no more than the measured
value plus the uncertainty and no less than the measured value minus the uncertainty".
In summary, Lecture 01 establishes that understanding uncertainty is fundamental to the
concept of measurement in physics. It differentiates between a simple reading and a
meaningful measurement, which must include an estimation of its uncertainty. The lecture
uses various examples to illustrate that uncertainty arises from the limitations of
measuring instruments, experimental conditions, and physical constraints. Finally, it
introduces the formal representation of uncertainty as an interval of confidence around the
measured value. The lecture concludes by stating that future lectures will delve into how to
determine and use these uncertainties in calculations. There were no specific equations or
questions posed to the audience in this introductory lecture.
Lecture 02 of the AS Physics 9702 series by Sir Faizan Pasha transitions from the
fundamental concept of uncertainty in measurements (covered in Lecture 01) to how
uncertainty is dealt with in examination contexts and how it propagates through calculations.
Main Points:
●​ Exam Expectations: The lecture starts by addressing what to expect regarding
uncertainty in exams. Questions will likely involve measurements given with their
associated uncertainties, and you will be asked to perform calculations using these
measurements, subsequently needing to determine the uncertainty in your calculated
result.​
●​ Example Calculation: Volume of a Cylinder: To illustrate this, Sir Faizan presents
an example of a uniform cylinder with a given height and diameter, each with an
associated uncertainty:​
○​ Height (h) = 18.9 ± 0.1 cm
○​ Diameter (d) = 2.34 ± 0.01 cm
○​ The question asks to calculate the volume of the cylinder using this
information.
●​ Formula Manipulation: The lecturer emphasises the importance of using the
formula for volume in terms of the given variables (height and diameter) rather than
radius. Since the volume of a cylinder is V = πr²h and radius (r) = d/2, the formula is
rewritten as V = π(d/2)²h = V = (π/4)d²h.​
●​ Calculating the Value: The numerical value of the volume is then calculated by
substituting the given values for diameter and height into the modified formula: V =
(π/4) * (2.34 cm)² * (18.9 cm) ≈ 81.2 cm³.​
●​ Difference Between Measured and Calculated Values: Sir Faizan highlights a
crucial distinction: the height and diameter are measured values obtained using
measuring devices, whereas the volume is a calculated value derived using a
formula and the measured quantities.​
●​ Uncertainty in Calculated Values: The central question posed is: if the measured
quantities (height and diameter) have uncertainties, what is the uncertainty in the
calculated quantity (volume)? The lecture states that since the height and diameter
have uncertainties, the calculated volume will also have some degree of uncertainty.
Determining this uncertainty in calculated values based on the uncertainties of the
measured values is a key learning outcome for this chapter.​
●​ Notation for Uncertainty: The symbol is δ introduced as the standard notation for
absolute uncertainty. For a quantity L with an uncertainty δ L, it is written as L ± δ
L. For example, the height would be written as h ± δ h.​
●​ Fractional Uncertainty: Fractional uncertainty is defined as the ratio of the
absolute uncertainty to the measured or calculated value: Fractional Uncertainty =
δ Q / Q, where Q is the quantity and δ Q is its absolute uncertainty. If this is for length
(L), it would be δ L / L.​
●​ Percentage Uncertainty: Percentage uncertainty is simply the fractional
uncertainty multiplied by 100: Percentage Uncertainty = (δQ / Q) * 100%.​
●​ Importance of Different Types of Uncertainty: The lecturer explains that
sometimes a question might ask for absolute uncertainty, fractional uncertainty, or
percentage uncertainty, so it's essential to understand how to calculate each. He
provides an example to illustrate why percentage uncertainty can be more useful for
comparing the precision of different measurements, especially when the magnitudes
of the measurements are vastly different. In the example, a small absolute
uncertainty in the length of a pencil might represent a larger percentage uncertainty
than a larger absolute uncertainty in a long distance.​
●​ Rules for Combining Uncertainties (Equations): The core of the latter part of the
lecture introduces several rules (equations) for how uncertainties combine when
quantities are added, subtracted, multiplied, or divided, or raised to a power. These
rules are presented with the caveat that they might look intimidating initially, but they
are essential for solving exam problems.​
○​ Addition: If u = x + y, then the absolute uncertainty in u is Δu = Δx + Δy.
○​ Subtraction: If u = x - y, then the absolute uncertainty in u is also Δu = Δx +
Δy. (Uncertainties always add, they never subtract).
○​ Multiplication by a Constant: If u = c * x (where c is a constant), then the
absolute uncertainty in u is Δu = |c| * Δx, and the fractional uncertainty in u is
Δu / u = Δx / x (the fractional uncertainty remains the same).
○​ Multiplication of Variables: If u = x * y * z, then the fractional uncertainty in u
is Δu / u = Δx / x + Δy / y + Δz / z.
○​ Division of Variables: If u = x / y, then the fractional uncertainty in u is Δu / u
= Δx / x + Δy / y.
○​ Quantity Raised to a Power: If u = c * xⁿ * yᵐ / zᵖ, then the fractional
uncertainty in u is Δu / u = |n| * (Δx / x) + |m| * (Δy / y) + |p| * (Δz / z). Note
that the constant 'c' does not contribute to the fractional uncertainty.
●​ Learning the Rules: The lecturer stresses the importance of memorising and
understanding these rules. He suggests writing them down and reviewing them
regularly. The analogy of learning the quadratic formula in mathematics is used to
encourage students to accept and learn these rules, with the promise that their
application will become clearer in subsequent lectures.​
Example Question (Implicit):
While no explicit question is posed to the students to solve during this lecture excerpt, the
entire setup with the cylinder and its dimensions with uncertainties serves as an implicit
example that will likely be followed up with a question in future lectures: "Calculate the
volume of the cylinder and its associated uncertainty.". This would require using the
volume formula derived (V = (π/4)d²h) and the appropriate uncertainty propagation rules for
multiplication and powers to find the uncertainty in the calculated volume.
In summary, Lecture 02 introduces the application of uncertainty concepts in calculations
and exams. It defines absolute, fractional, and percentage uncertainties and lays down the
fundamental rules for how uncertainties propagate when mathematical operations are
performed on measured quantities. The example of the cylinder volume calculation sets the
stage for applying these rules in subsequent lectures.