SAJC Physics Summary for 2025 JC1 FE for students

SAJC H2 Physics Summary updated Oct 2025 1/38 PHYSICS H2 Physics Summary St Andrew’s Junior College H2 Name: ________________ Class: _________

SAJC H2 Physics Summary updated Oct 2025 2/38 Data speed of light in free space c = 3.00 x 108 m s-1 gravitational constant G = 6.67 x 10-11 N m2 kg-2 acceleration of free fall g = 9.81 m s-2 Formulae uniformly accelerated motion s = u t + 1 2 a t2 v2 = u2 + 2 a s pressure p = F A gravitational potential  = − Gm r displacement of particle in s.h.m. x = xo sin  t velocity of particle in s.h.m. v = v0 cos  t =   22 0 xx −

SAJC H2 Physics Summary updated Oct 2025 3/38 H2 Physics Summary (Syllabus 9478) (Definitions, Equations, Terms, Qualitative Explanations, Common Mistakes) Key: ( ) optional but good to include; { } Tutor’s comments/Common Mistakes; [ ] Alternative Term Topic 1: Quantities and Measurements 1. Base quantities (with their SI base units/ symbol): length (metre/ m), mass (kilogram/ kg), time (second/ s), amount of substance (mole/ mol), temperature (kelvin/ K), current (ampere/ A). Base units: are (a choice of well-defined) units by which all other units are expressed. Derived unit: a unit expressed as a product and/or quotient of the base units. (eg. newton, pascal, joule, watt, hertz, coulomb, volt, ohm) Unitless quantities: all numbers, trigo functions, log functions (logx, ln), powers, certain physical constants (eg. refractive index) 2. Homogeneous equations: An equation is homogeneous if every term on both sides of the equation have the same SI base units. A physically correct equation must be homogeneous. 3. Prefixes: to recall certain prefixes & their decimal equivalents: • 1012 tera (T), 10 9 giga (G), 10 6 mega (M), 103 kilo (k), 10 -1 deci (d), 10 -2 centi (c), 10 -3 milli (m), 10 -6 micro (), 10-9 nano (n), 10-12 pico (p). • Sample TYS qns: decimetre = 10-1 m; megametre = 106 m; 500 cN = 500 x 10-2 N (2016 P1Q1) 4. Making reasonable estimates of certain physical quantities: • to give the figure to 1 significant figure. {N08P1Q2, N09P1Q2} • need to express a more complicated quantity in terms of other simpler quantities using a formula first. • 'correct to an order-of-magnitude' means value quoted is reliable to within a factor of ten or so. • Significant figures: rules to follow: • All non-zero digits are significant digits • Zeros that occur between significant digits are significant digits • Zeros to the right of the decimal point and to the right of a non -zero digit are significant 5. Errors • An error is the difference between the measured value and the ‘true value’. A total error can be a combination of both systematic error and/or random error. 6. Random error: • An error {not reading} which causes measurements to be sometimes larger than the true value and sometimes smaller than the true value. • It is equally likely to be positive or negative with respect to true value, and can have different magnitudes. • Can be reduced (eg. by taking the average of repeated readings, or by plotting a graph to obtain the line or curve of best fit (Note: presence of random errors is represented by the scattering of points about the best-fit line)). • Eg. parallax error, non-uniform diameter of wire. 7. Systematic error: • An error {not reading} which causes measurements to be either, always larger than the true value , or always smaller than the true value. Hence in an expt, a systematic error is of the same magnitude & with the ‘same sign’. • Cannot be reduced by taking the average of repeated measurements. • Can be eliminated {for eg, if a faulty instrument is replaced, if the experimental technique/procedure is improved, or a different experimental approach is used}. • Eg. zero error, incorrect calibration of the scale.

SAJC H2 Physics Summary updated Oct 2025 4/38 8. Accuracy: • refers to the degree of agreement between the result of a measurement and the true value of the quantity. • Note: If several readings of a quantity are taken, the “result of the measurement” refers to the mean (average) value of the readings. We take the average of the readings and compare it with the true value to see if it is accurate. • is a measure of the magnitude of the systematic error present; high accuracy implies a small systematic error. • check by looking at average value in a table or if gradient or y-intercept agree with the equation in a graph. 9. Precision: • refers to the degree of agreement [scatter, spread] of repeated measurements of the same quantity. {Note: regardless of whether or not they are correct with respect to the true value.} • is a measure of the magnitude of the random errors present; high precision implies a small random error. • check by looking at how close the repeated values are in a table or if the data scattering is close to the best fit line in a graph. 10. For a quantity x = (2.0  0.1) mm, Actual [Absolute] uncertainty, x = 0.1 mm Fractional uncertainty, x x Δ = 0.05 Percentage uncertainty, x x Δ  100% = 5 % 11. To determine the overall (compound/consequential) uncertainty Y that is measured from other quantities, we follow the steps: • Make the required quantity the subject of the equation (Sometimes the equation has to be deduced, if not already given by question) • Categorise the problem (purely +/- or / for simple equations OR complex equations) • Decide on the method (Rules 1, 2, 3) • Calculate the value of the unknown quantity (leave in many s.f. first) • Calculate and express the uncertainty (e.g. ∆Y) to 1 s.f. • Write the calculated value (Y) to the same place value as the uncertainty (∆Y). Express answer to standard form (not always compulsory but good practice)

SAJC H2 Physics Summary updated Oct 2025 5/38 Here is an overview of the 3 Rules: Rule 1 Rule 2 Rule 3 Add or subtract (for simple equations) Multiply, divide or power (for simple equations) (for complex equations) Sum all contributing absolute uncertainties If Y = nA + mB, (n & m are constants),  Y = |n|A + |m|B Note: Retain the coefficients Sum all contributing fractional uncertainties If mnZaXY = , (a, n & m are constants)  Z ZmX XnY Y += Note: Coefficient a is ignored as it is considered error-free. Power n (or m): bring down, modulus it, and treat it as coefficient! Calculate the maximum and minimum of the quantity Y. Then determine the absolute uncertainty Y.  Y = ½ (Ymax –Ymin) 12. For Practical Exam (not theory papers): Absolute Uncertainty is generally estimated to: (a) 1 x smallest div of instrument if conditions of measurement are ‘ideal’ (Exceptions: stopwatch timing where precision is 0.1 s; analogue meters, measuring cylinder, thermometer (steady temp) where ½ smallest division is required instead) (b) In general, x = (3 to 5) x smallest div if circumstances of measurement are ‘challenging’. 13. Actual uncertainty must be recorded to only 1 significant figure (1 sf). The number of sig fig to be recorded for a calculated quantity x is determined by the position of the last digit of its actual error x. Eg: If g has been calculated to be 9.80645 m s-2 & g has been calculated to be 0.04848 m s-2, then, g should be recorded as 0.05 m s-2 {1 sf } & g must then be recorded as (9.81  0.05 ) m s-2. If g = 1.23 m s-2, then g should be recorded as (10  1) m s-2. If the actual uncertainty is recorded (to 1sf) to its tenth or hundredth place , the number of sf for its calculated quantity should follow to its tenth or hundredth place respectively