Y3 Y4 ACSI IP Physics Chapter 1

CORE NOTES CHAPTER 1: MEASUREMENTS By: Oscar Chiang Page 1 - Part I: Physical Quantities and SI Units A physical quantity is a quantity that can be measured. It consists of a numerical magnitude and a unit. Base Quantity SI Unit Length metre (m) Mass kilogram (kg) Time second (s) Electric current ampere (A) Thermodynamic temperature kelvin (K) Luminous intensity candela (cd) Amount of substance mole (mol) A derived quantity is derived from the seven base quantities. The following table show a few examples of derived quantities. Derived Quantity SI Unit Area Metre (m2) Volume Cubic metre (m3) Speed Metre per second (m s-1) Scalar quantities have magnitude only. (e.g. distance, speed, temperature, mass, volume, density, pressure, energy, power, time) Vector quantities have both magnitude and direction. (e.g. displacement, velocity, acceleration, weight, force) - Part II: Prefixes and Standard Form Standard form is scientific notation. e.g. 100000 à 1.0 × 10! Examples Express 50 metres per second in scientific notation. 50ms-1 Express 2500 ms-1 in km h-1. ms-1 = !"""# (!&#)()""* (! +,-.) = /!0 2500ms-1 = 2500 × !0/ = 9000km h-1 Express J in SI base units. 𝐸"=12𝑚𝑣# 𝐽=𝑘𝑔(𝑚𝑠$%)# 𝐽=𝑘𝑔𝑚#𝑠$# Factor Equivalent Prefix Symbol 109 1000000000 giga- G 106 1000000 mega- M 103 1000 kilo- k 10-1 0.1 deci- d 10-2 0.01 centi- c 10-3 0.001 milli- m 10-6 0.000001 micro- μ 10-9 0.000000001 nano- n Tip: Remember M for million, which has 6 zeros as well.

By: Oscar Chiang Page 2 - Part III: Errors There are 2 types of errors that can exist in experiments, random error and systematic error. • Random Errors include parallax errors, unfixed patterns, etc. Accuracy can be corrected by repeating the experiments a few times. • Systematic Errors Systematic Errors are errors that are usually from measuring instruments such as the zero error in vernier calipers and micrometer screw gauge. This can be easily removed. Vernier caliper (precision 0.01cm) zero error Micrometer screw (0.01mm) gauge zero error - Part IV: Precision Precision is half the smallest division Precision is the smallest division Measuring Cylinder Metre Rule Thermometer Protractor Spring Balance Stopwatch (Electronic à consider HRT1) Ammeter Micrometer screw gauge (0.01mm) Voltmeter Vernier Caliper (0.01cm) When data are added or subtracted, the final answer should follow the data with the smallest number of decimal place. e.g. 5.0 + 2.25 = 7.3 (1d.p.) When data are multiplied or divided, the final answer should follow the data with the smallest number of significant figures. e.g. 5.0 × 2.25 = 11 (2s.f.) When finding average, the calculated answer should follow the same precision as the measuring instrument. The reason for this is that the calculated value should not be more accurate than the least accurate measured data. If calculation is using a constant with no exact precision, do not follow the constant’s SF or DP. e.g. Time taken for 20 oscillations is 37.9s. Time taken for 1 oscillation = &'.)#* = 1.89s (Not 1.9s!!) 1 HRT is Human Reaction Time which the number is rounded to 1 decimal place. No error Positive zero error Negative zero error Add to your calculations: 0cm Add to your calculations: -0.03cm Add to your calculations: +0.02cm Thimble scale Add to your calculations: 0mm Add to your calculations: -0.02mm Add to your calculations: +0.04mm

By: Oscar Chiang Page 3 - Part V: Recording Data in a Table There should be a consistent number of decimal places which reflects the precision of the instrument on the table. There should also be units in the headings in the title of the table. (e.g., t1 / s) The independent variable should have values of equal increment. - Part VI: Graph Graphs are graded according to the scale, title, axis, points and line. • Scale Use scales that are well spread out on the entire graph paper. • Title Graph of ( y/unit ) against (x /unit). • Axis Label axis with symbol and units. • Points Plot the points as accurate as possible, with crosses. • Line Shift the ruler till it passes through the most number of points. If some plots cannot be on the line, ensure that these plots are equally positioned on each side of the line. If there are about an equal number of points below and above the line, it is still the best-fit line. • Evidence / Conclusion of Graph If it does not pass through the origin (0,0) but slopes up from left to right, it is linearly related. If it does not pass through the origin (0,0) but slopes up from right to left, it is linearly related with a negative constant. If it passes through the origin (0,0), the graph is directly proportioned. Graph of y/mm against x/mm