Physics P1, P2

Since superscript letters doesn't seem to be supported here (Exception are presets), please take note that the [^] sign translates to 'to the power of'. (e.g. 10^-6 means ten to the power of minus six)

Random General Tips

• DON'T PANIC (Printed in large, friendly, and yellow letters)
  
• Be concise, precise, accurate, clear, complete, and coherent when you are asked to define. (This is also why definitions are the hardest things in physics. Believe me)
• Use multiple short sentences for definitions, one point per sentence. This way, your answer is direct and easily understood. (As your English sucks, you are more likely to obscure the meaning should you put long sentences)
• In diffraction grating, n is always rounded down to the lowest integer. (e.g. n =2.8, so when rounded, it becomes n = 2, not n = 3)
• Read, comprehend, and read again the question. Seriously.
  
• When encountering an unfamiliar sum, the first thing that you must do is to find out which laws to apply to the sum. This is extremely important. (For proof, read question number 2bii, paper 2, physics, summer 2008; was your first thought the principle of conservation of momentum?) Second, attack the sum in a logical manner; never ever ever ever assume anything, and always start from facts given by the sum. Third, a particular sum could involve materials from any chapters, so don't be so narrow-minded and confine your thinking in only one direction; be creative.
• Sometimes, they require you to write the equations in words first (i.e. Work done = area under graph line) before moving on to symbols. (i.e. W = ½Fx) This usually appears when you are asked to prove something.
• When drawing field lines, draw at least (To 6.
  
• May/June 2006's Paper 2 is one of the hardest in the repertoire, (But honestly, I think it is the hardest) so go check that.
  

Chapter 1 - Physical Quantities and Units

All quantities consist of a numerical magnitude and a unit.

The six basic units (In S.I. units) are:

• mass (kg)
• length (m)
• time (s)
• current (A)
• temperature (K)
• amount of substance (mol)

Derived units consists of basic units. (e.g. Velocity is displacement over time [m/s], charge is current times time [As])

Physical equations must be homogeneous. Examples:

• v = u + at (Homogeneous; v is [m/s], u is [m/s], at is [(m/s²)*s] = [m/s])
• v² = u² + 2at (Not homogeneous; v² is [(m/s)²] = [m²/s²], u² is [(m/s)²] = [m²/s²], 2at is [(m/s²)*s] = [m/s])

List of prefixes:

• pico [p] = 10^-12
• nano [n] = 10^-9
• micro [μ] = 10^-6
• mili [m] = 10^-3
• centi [c] = 10^-2
• deci [d] = 10^-1
• kilo [k] = 10^3
• mega [M] = 10^6
• giga [G] = 10^9
• tera [T] = 10^12

Should you ever need to estimate physical quantities, there are 2 things that you must do: 1) Use your common sense, and 2) Common sense.

Scalar quantities have only magnitude and unit, while vector quantities have magnitude, direction, and unit. (e.g. Energy [J], Distance [m] are scalars; force [N], momentum [Ns] are vectors)

In doing equations, the product or division of two vector quantities would result in a scalar quantity, while the product or division of a scalar and a vector quantity would result in a vector quantity. (e.g. Force (Vector) times displacement (Vector) equates to energy (Scalar), acceleration (Vector) times time (Scalar) equates to velocity (Vector))

Vectors can be added or subtracted only if they are coplanar. (i.e. On the same plane; vectors in the x-direction can be added or subtracted, but not vectors in x-direction with vectors in y-direction)

If wishing to add non-coplanar vectors, it is necessary to split the vectors into perpendicular components. (Most of the time, into x-and-y-directions)

Chapter 2 - Measurement Techniques

Formulae in this chapter:

• Δa/a = Δb/b + Δc/c + ... + Δz/z (Fractional uncertainty)
  

Systematic errors,

• causes a set of readings to be either too high or too low from the true value.
• cannot be eliminated or reduced by averaging.
• include: Unaccounted zero error in measuring instrument; using a damaged or poorly calibrated instrument; reaction time not accounted for. (e.g. When using stopwatches)

Random errors,

• causes a set of readings to have generally high scatter. However, the end result could still be accurate.
• can be reduced by averaging.
• include: Parallax error, changes in wind speed and/or direction, changes in temperature, fluctuations in pressure, etc.

Precision refers to the distribution or scatter of values about the true value. A set of readings is said to be precise if it has low scatter.

Accuracy refers to the trueness of values. A set of readings is set to be accurate if the readings are about the true value of the reading.

Therefore, a set of values with very few random errors can be said to be precise, while a set of values with negligible systematic error can be said to be accurate.

Example: (Doing an experiment to find the value of g)

• g = 8.93, 9.34, 9.01, 8.77 (Not precise and not accurate)
• g = 9.34, 9.35, 9.33, 9.34 (Precise, but not accurate)
• g = 9.66, 9.81, 9.99, 9.78 (Not precise, but accurate)
• g = 9.79, 9.82, 9.81, 9.81 (Precise and accurate)

Uncertainty arises because a quantity may never be measured exactly. (e.g. Even if it looks like you've measured 25 cm on a plastic ruler, the actual value could be 25.0012312753 cm)

The uncertainty of a measurement usually is taken from the smallest scale of the measuring instrument (e.g. Suppose you've measured 24.3 mm on the vernier caliper. The smallest reading the vernier caliper can take is 0.1 mm, therefore, the reading is written as: 24.3 ± 0.1 mm. This means that the exact value of the reading is between 24.2 to 24.4 mm)

The fractional uncertainty of a measurement is the ratio of the uncertainty of the measurement over the read value. (Using the above example, its fractional uncertainty is given by [Δx/x] = [0.1/24.3])

The percentage uncertainty of a measurement is its fractional uncertainty expressed in percentage form. (Again, using the above example, the percentage uncertainty is given by [(Δx/x)*100%] = [(0.1/24.3)*100%])

When arithmetically operating on readings with uncertainties, always apply the fractional uncertainty formula. [Δa/a = Δb/b + Δc/c + ... + Δz/z, where Δa represents the uncertainty of quantity a, Δb quantity b, and so on]

For example, you are asked to find the answer of [(5 ± 1)*(7 ± 2)]:

• Δa/a = Δb/b + Δc/c
• (Δa/35) = (1/5) + (2/7)
• Δa = 17
• Answer = 35 ± 17

The 5 and 7 are multiplied as usual, but this is not the case with the uncertainty. This is why it is recommended to stick to the formula.

When measuring distance using a ruler, you are actually measuring two points and taking the difference between those two points. Therefore, the uncertainty should be doubled. (e.g. Smallest scale on ruler is 1 mm. You measured 250 mm. The uncertainty would be 250 ± 2 mm)

Chapter 15 - Waves

The electromagnetic spectrum:

• Gamma-rays (10^-14 < λ m < 10^-11)
• X-rays (10^-11 < λ m < 10^-8)
• Ultraviolet (10^-11 < λ m < 4 * 10^-7)
• Visible light (3.8 * 10^-7 < λ m < 7.5 * 10^-7)
• Infra-red (7.5 * 10^-7 < λ m < 10^-3)
• Microwaves (10^-3 < λ m < 1)
• Radio waves (1 < λ m < 10^9)