Base Quantities   SI Units  Name  Symbol  Length  metre  m  Mass  kilogram  kg  Time  second  s  Amount of substance  mole  mol  Temperature  Kelvin  K  Current  ampere  A  Luminous intensity  candela  cd  Derived units as products or quotients of the base units: Derived  Quantities Equation  Derived Units  Area (A)  A = L^{2}  m^{2}  Volume (V)  V = L^{3}  m^{3}  Density (ρ)  ρ = m / V  kg m^{3}  Velocity (v)  v = L / t  ms^{1}  Acceleration (a)  a = Δv / t  ms^{1} / s = ms^{2}  Momentum (p)  p = m x v  (kg)(m^{s1}) = kg m s^{1}  Derived Quantities  Equation   Derived Unit  Derived Units  Special Name  Symbol  Force (F)  F = Δp / t  Newton  N  [(kg m s^{1}) / s = kg m s^{2}  Pressure (p)  p = F / A  Pascal  Pa  (kg m s^{2}) / m^{2} = kg m^{1} s^{2}  Energy (E)  E = F x d  joule  J  (kg m s^{2})(m) = kg m^{2} s^{2}  Power (P)  P = E / t  watt  W  (kg m^{2} s^{2}) / s = kg m^{2} s^{3}  Frequency (f)  f = 1 / t  hertz  Hz  1 / s = s^{1}  Charge (Q)  Q = I x t  coulomb  C  A s  Potential Difference (V)  V = E / Q  volt  V  (kg m^{2} s^{2}) / A s = kg m^{2} s^{3} A^{1}  Resistance (R)  R = V / I  ohm  Ω  (kg m^{2} s^{3} A^{1}) / A = kg m^{2} s^{3} A^{2}  Prefixes and their symbols to indicate decimal submultiples or multiples of both base and derived units: Multiplying Factor  Prefix  Symbol  10^{12}  pico  p  10^{9}  nano  n  10^{6}  micro  μ  10^{3}  milli  m  10^{2}  centi  c  10^{1}  decid  d  10^{3}  kilo  k  10^{6}  mega  M  10^{9}  giga  G  10^{12}  tera  T  Estimates of physical quantities: When making an estimate, it is only reasonable to give the figure to 1 or at most 2 significant figures since an estimate is not very precise. Physical Quantity  Reasonable Estimate  Mass of 3 cans (330 ml) of Coke  1 kg  Mass of a mediumsized car  1000 kg  Length of a football field  100 m  Reaction time of a young man  0.2 s   Occasionally, students are asked to estimate the area under a graph. The usual method of counting squares within the enclosed area is used. (eg. Topic 3 (Dynamics), N94P2Q1c)
 Often, when making an estimate, a formula and a simple calculation may be involved.
EXAMPLE 1: Estimate the average running speed of a typical 17yearold‟s 2.4km run. velocity = distance / time = 2400 / (12.5 x 60) = 3.2 ≈3 m s^{1} EXAMPLE 2: Which estimate is realistic?  Option   Explanation  A  The kinetic energy of a bus travelling on an expressway is 30000J   A bus of mass m travelling on an expressway will travel between 50 to 80 kmh^{1}, which is 13.8 to 22.2 ms^{1}. Thus, its KE will be approximately ½ m(182) = 162m. Thus, for its KE to be 30000J: 162m = 30000. Thus, m = 185kg, which is an absurd weight for a bus; ie. This is not a realistic estimate.  B  The power of a domestic light is 300W.   A single light bulb in the house usually runs at about 20W to 60W. Thus, a domestic light is unlikely to run at more than 200W; this estimate is rather high.  C  The temperature of a hot oven is 300 K.   300K = 27 0C. Not very hot.  D  The volume of air in a car tyre is 0.03 m3.  (http://www.xtremepapers.com/images/alevel/physics/measurement/volume_of_air_in_a_car_tyre_is_0_03_m_3.png)[/t][/t] 
[/t] Estimating the width of a tyre, t, is 15 cm or 0.15 m, and estimating R to be 40 cm and r to be 30 cm, volume of air in a car tyre is = π(R^{2} – r^{2})t = π(0.4^{2} – 0.3^{2})(0.15) = 0.033 m^{3} ≈ 0.03 m^{3} (to one sig. fig.)  Distinction between systematic errors (including zero errors) and random errors and between precision and accuracy: Random error: is the type of error which causes readings to scatter about the true value. Systematic error: is the type of error which causes readings to deviate in one direction from the true value. Precision: refers to the degree of agreement (scatter, spread) of repeated measurements of the same quantity. {NB: regardless of whether or not they are correct.} Accuracy: refers to the degree of agreement between the result of a measurement and the true value of the quantity.   → → R Error Higher → → → → → → Less Precise → → →  ↓ ↓ ↓ S Error Higher Less Accurate ↓ ↓ ↓[/t][/t] 
[/t] (http://www.xtremepapers.com/images/alevel/physics/measurement/true_value_01.png)  (http://www.xtremepapers.com/images/alevel/physics/measurement/true_value_02.png)  (http://www.xtremepapers.com/images/alevel/physics/measurement/true_value_03.png)  (http://www.xtremepapers.com/images/alevel/physics/measurement/true_value_04.png)  Assess the uncertainty in a derived quantity by simple addition of actual, fractional or percentage uncertainties (a rigorous statistical treatment is not required). For a quantity x = (2.0 ± 0.1) mm, Actual/ Absolute uncertainty, Δ x = ± 0.1 mm Fractional uncertainty, Δxx = 0.05 Percentage uncertainty, Δxx 100% = 5 % If p = (2x + y) / 3 or p = (2x  y) / 3 , Δp = (2Δx + Δy) / 3 If r = 2xy^{3} or r = 2x / y^{3} , Δr / r = Δx / x + 3Δy / y Actual error must be recorded to only 1 significant figure, & The number of decimal places a calculated quantity should have is determined by its actual error. For eg, suppose g has been initially calculated to be 9.80645 ms^{2} & Δg has been initially calculated to be 0.04848 ms^{2}. The final value of Δg must be recorded as 0.05 ms^{2} {1 sf }, and the appropriate recording of g is (9.81 ± 0.05) ms^{2}. Distinction between scalar and vector quantities:  Scalar  Vector  Definition  A scalar quantity has a magnitude only. It is completely described by a certain number and a unit.  A vector quantity has both magnitude and direction. It can be described by an arrow whose length represents the magnitude of the vector and the arrowhead represents the direction of the vector.  Examples  Distance, speed, mass, time, temperature, work done, kinetic energy, pressure, power, electric charge etc. Common Error: Students tend to associate kinetic energy and pressure with vectors because of the vector components involved. However, such considerations have no bearings on whether the quantity is a vector or scalar.  Displacement, velocity, moments (or torque), momentum, force, electric field etc.  Representation of vector as two perpendicular components: In the diagram below, XY represents a flat kite of weight 4.0 N. At a certain instant, XY is inclined at 30° to the horizontal and the wind exerts a steady force of 6.0 N at right angles to XY so that the kite flies freely.
(http://www.xtremepapers.com/images/alevel/physics/measurement/representation_of_a_vector.png) By accurate scale drawing  By calculations using sine and cosine rules, or Pythagoras‟ theorem  Draw a scale diagram to find the magnitude and direction of the resultant force acting on the kite. (http://www.xtremepapers.com/images/alevel/physics/measurement/representation_of_a_vector_by_scale_drawing.png)[/t][/t] 
R = 3.2 N (≡ 3.2 cm) at θ = 112° to the 4 N vector.[/t] (http://www.xtremepapers.com/images/alevel/physics/measurement/representation_of_a_vector_using_sine_and_cosine_rules.png) Using cosine rule, a^{2} = b^{2} + c^{2} – 2bc cos A R^{2} = 42 + 62 2(4)(6)(cos 30°) R = 3.23 N Using sine rule: a / sin A = b / sin B 6 / sin α = 3.23 / sin 30° α = 68° or 112° = 112° to the 4 N vector   Summing Vector Components  (http://www.xtremepapers.com/images/alevel/physics/measurement/representation_of_a_vector_summing_components.png)[/t][/t] 
[/t] F_{x} =  6 sin 30° =  3 N Fy = 6 cos 30°  4 = 1.2 N R = √(3^{2} + 1.2^{2}) = 3.23 N tan θ = 1.2 / 3 = 22° R is at an angle 112° to the 4 N vector. (90° + 22°)  








